[Redmi Note 2 Q&A, Help & Troubleshooting] beokabatukaba:
Sounds like you're having issues similar to what I had. Never fear! I am in almost the exact same situation.

I got mine from GearBest last September shortly after it came out because it was such a good deal for the hardware you get. However, I knew ahead of time, and I'm sorry to tell you, that it will not work with T-mobile's 4G LTE. It will, however, work with T-Mobile's HSPA+ (I think it's still considered 3G but it's also sorta better than 3G? Every cell provider uses the same names to refer to totally different technologies, so it's all very confusing.). HSPA+ is more than enough for me; you can still stream 1080p video without buffering as long as you've got a good signal. Maybe web pages won't load instantaneously, but whatever.

My main issue right off the bat was that there was some preinstalled app absolutely draining my battery. The phone was hot most of the time and died by mid afternoon with limited usage. So I needed to fix it.

I'm inferring from your request that you haven't yet tried to root the device. This is the main way I know of to fix your problems. It will allow you to install any of the custom ROMs people share on this site as well as manage preinstalled apps and utilize other apps on the play store that require a rooted device to work.

Disclaimer: Google around and visit other guides for custom ROM installation before you follow this. I may have missed something as I'm typing this up mostly from memory. Your milage may vary, and it's important to make absolutely sure that you know what you're doing so as to avoid bricking your phone.

Basically, all you need to do is:

0. Make sure you have an SD card. I don't know if it's a necessity or not, but it's useful for keeping data like music, backups, and other ROMs stored where the data doesn't need to get wiped every time you install a new ROM.

1. Find the ROM you want to use. I am currently using MoKee by Bule because I've been having battery troubles with virtually every other ROM for some unknown reason. I'd also recommend the official Xiaomi.eu international ROM if you want to continue using MIUI, or Daniel's CM 12.1. Put the downloaded zip onto your SD card. If you don't have an SD card, you'll have to find another guide to help.

3. If necessary, visit openGapps to download the google apps you need to access the play store. Some ROMs come with it, some don't. The ROM's page should tell you. Put it next to the ROM on your phone.

2. Follow this guide to install the MiFlash tool (which you won't necessarily use) which will install all the drivers you need to flash TWRP. You don't necessarily need SuperSU (I don't have it installed), especially if you don't want to mess around with a lot of apps that require a rooted device. Every ROM I've used has some form of built-in root management (though I'm by no means a professional with this stuff).

3. Boot into recovery as suggested in the guide. Go to wipe, advanced wipe and select everything except for Micro SDCard. Swipe to Wipe.

4. Go back to home, install, select storage, Micro SDCard, and find wherever you put the zip of the ROM you downloaded. Select it and Swipe to confirm Flash.

5. If necessary, repeat for the google apps zip.

6. It should take a minute or two to install. Clear cache/dalvik cache if it gives you that option and then reboot the device.

YAY, you should have a clean, functional device free from most Chinese bloatware although this depends on which ROM you install. Some are still Chinese by default but should have readily accessible English options upon startup. Sometimes you need to reboot after selecting English and finishing the startup in order for a few of the Chinese characters to switch to English for some reason. If the default keyboard is still wacky, do your best to make your way to the play store and install google keyboard or whatever other option you desire.

Hope this works!