Given a travel related situation, and given a specific question about the situation, summarize the question into a title

Input: Consider Input: I am a US passport holder (living in Canada) traveling from Canada to Ecuador with connections in the US via multiple airlines. I'm worried that some of my layovers might be a bit too tight. To help plan, I'm trying to find out when, where, and how many times I'll have to check luggage and have security checks.

This was all purchased on a single ticket through Cheap O Air.

Here's my itinerary:

Edmonton, Canada (YEG) -> Las Vegas, USA (LAS) Airline: WestJet
Departure: 8:30 AM, Arrival: 10:30 AM

-Layover time: 1:48-

Las Vegas, USA -> Miami, USA (MIA) Airline: American Airlines
Departure: 12:18 PM, Arrival: 8:07 PM

-Layover time: 1:23-

Miami, USA -> Quito, Ecuador (UIO) Airline: LATAM Airlines
Departure: 9:30PM, Arrival: 12:45Am (next day)

Questions:

Will I have to baggage check for each airline? And does that mean I have to leave the gates for each check and do security each time? If not, where and when can I expect those things to happen?

Also, I did an online chat with a Cheap O Air representative, and the he assured me that I would only need to do baggage check and security at YEG and not at my connections in the US. That sounds too good to be true to be honest and I don't know if I believe him.

Output: Canada to South America with connections in US with multiple airlines, where will I do security/baggage check?

Input: Consider Input: I'm traveling to Iran and i need to bring my laptop.

For western standards I do not have anything illegal on my hard drive but since I'm not familiar with the Sharia I'm a little bit paranoid.

Is it dangerous to have, for example, holiday pictures of girls in bikinis or similar on your laptop? Is it common that laptops get searched or am I just paranoid?
If that is dangerous, how should I proceed? I need to take my laptop with me. Should I encrypt everything? Given the fact that browsing the internet already caches maybe dangerous pictures and it is very hard to be sure that one has deleted all of them, how should I clean my laptop?

Output: Laptop/mobile device in countries with Sharia

Input: Consider Input: I will be visiting Jerusalem in a week. Is Israeli government allow to pray in Masjid Al-Aksa? Can I go there freely? Is there anything I should know before I go there?
Output: Possibility of praying in Masjid Al-Aqsa (Jerusalem)