I know this is a late reply, but you ask a lot of questions lots of people ask. And since im passionate about the subject...:

Q: Who is to decide the amount of that? There are two main aspects to this.
A: The goal is to eliminate or at least severly reduce the number of individuals living in poverty, or a basic needs package of sorts (emphasis on basic needs). So the povertly line is usually used as a guide. The first prevailing thought here is to peg it to the povertly line, which is already calculated annually by HHS. The second is to have a fixed rate that roughly equals the povertly line, but to periodically reassess it to bring it back up to par, sort of how we handle social security rates / minimum wage, etc. lastly, there is an equal distrobution of revenue. 2019 UBI tax generates 2.5T in revenue? the 250m adults get 10k in 2020.

I personally prefer the pegging to the poverty line. HHS sets the poverty line, and therefore the rate yearly, IRS dishes out the checks monthly. But thats just my opinion.

Q: How will it be decided when living cost is greatly ( or literally ) dependent on property pricing? Hence different location will have different living cost. Food, as in raw material assuming you cook yourself which is the cheapest option, could varies from state or even countries, but even if there is a 50% difference between the same items, the total amount spent on food will still be minimal. If you are allowed $4 per day and a 50% increase is only $2 increase, or $60 per month difference.
A: The intent is not to completely replace your needs, so this concern is not usually a factor taken into consideration when calculating a UBI. Your assumption that UBI would be more valuable or less valuable depending on where you live is correct, however is not a concern as the UBI should theoretcially be able to allow you to live _at_ the poverty line somewhere in the country, and therefore the choice to continue to live in poverty realative to your location is _theoretically_ a choice to continue your state.
A second answer to this is that states, and cities can adjust the UBI. A federal UBi is set to the federal poverty line, states can opt to charge an additional tax, and suppliment federal UBI with the tax revenue to only members of the states. Same for cities. So someone living in high plains of Wyominig may only receive the federal UBI, someone in LA could be receiving 3, Federal, Cali, and LA ubi's.

Q: Where as housing prices, rent will differ. Does UBI assumes I am going to live in remotely in small village? I dont have to live in a Citi, but I need somewhere to live while having the opportunities to find a job. And the future is heading towards megacities.
A: Assuming we live in the Federal Only UBI, the assumption is that your day to day will not change. If you currently live and work in the city, you will continue to. You may see some modest inflation in items like rent, however, you should be no _worse off_ than you currently are, but hopfully better off. UBI's goal is not to make it so no one ever has to work. That would be detrimental to society as we know it. The goal is to reduce the number of individuals living in poverty. So, UBI should _allow_ individuals who are forced into cities to leave, since many people follow the jobs as it were, those individuals that are content to live in BFE are welcome to, without the pressure of work. It should also allow individuals to reduce hours / be a single income family. Many parents would like to stay at home with the kids, but are unable to do so, or at least for a period of time. UBI will help reduce the income pressures we face today. But once again, COL in the city is not usually considered in factoring the UBI. If you live in a city, and you receive a UBI, there would likely be very little expectations of change for you. The individuals who it is suppsoed to help (homeless) should see a huge gain. They could pay for food, theoretically afford a buss ticket to a new town outside of the city center since they no longer need to beg, and get cheap rent to get their feet under them. In a year or two, they could choose relocate back to the cities with a career if they so choose, etc.
If we assume a local UBI to supliment the federal UBI, it is possible that you could quit working for an income and keep your current situation. But then agian, there would be less tax revenu to pay for the local UBI, which would mean

Statement: Basically what I am suggesting is, it is sort of pointless to discuss UBI or basic income guarantee without discussing housing. Which is not only the biggest expenses for living, but also the biggest asset class in our economy, and also the biggest problem.

Statement: I dont have an answer to those questions, but it just seems every time people discuss UBI or NIT ( Negative Income Tax ) or other BIG ( basic income guarantee ), we tends to ignore housing, or suggest hosting is not what BIG is hoping to solve. That is on the assumption with BIG people could basically live with sufficient food and water without dying if they are without jobs.

Comment: Housing costs are a huge part of the discussion, and are frquently discussed in the UBI circles. It is not ignored, however not the primary driver, and often not addressed in commentaries or summaries of the hugely complex subject. UBI is a wellfare program, full stop. Just as most of our wellfare programs are not designed to be an income replacement, but rather a suppliment, UBI is the same thing. For those of us who currently live in a high COL area, and shoose to do so, we will see very little difference in our day to day. Our bills will mostly stay the same, our jobs the same, and our expenses the same. We can expect that local price inflation, especially in the rent area, will most likely erase any gains we see from UBI. And that is OK, as we are not the ones UBI is implimented for. UBI is for the homeless, the overworked, and those who teeter at the povertly line. Its goal is to prevent a household from spiraling into a hole they cannot ever climb out of if they lose a job for a month. Like other wealfare programs, individuals may choose to use it as their sole means. There are housholds that use foodstamps as their sole source to purchase food with, or use the housing suppliments as their full rent checks. While the programs are not designed to be full replacements for these, some people make it work that way, and thats fine (depending on who you ask). UBI is simply a proposal to replace the many different and complicated and sometime unreliable wellfare programs with a single universal one. Some people may find a way to make UBI be their sole income source, and i look forward to seeing the creative things frugality will impliment. However for the overwhelming vast majority of us, nothing much will change. UBI should allow someone more mobility in the job market, should allow those in poverty a little more breathing room, should reduce the risk of starting your own business, could allow a household to leave the city if you wish since jobs dont keep them there. But for those of us living in a city apartment, (a little over half the country) we will see an additional ~$1k in our checking account each month, and probably an additional $500-$750/m in localized inflation (mostly in rents).