airport extreme vs airport express

Extreme is much better wireless router. It has the same specs as the Time Capsule but no hard disk.

Express is designed for airplay and is slow old N wireless design.

To improve signal in room 2 it is useless to place the Extreme or Express in there.. It will get no better speed than whatever you use now..

Any wireless repeater must be placed in a position where it picks up strong signals from the main router.. so about half way between the two rooms.

Wireless repeater systems are the worst way to fix problems though. It causes immediate slow down in the system as forcing the wireless to repeat will halve its speed at best.. and could be much worse.

Alternatives are using powerline adapters. These work well for many people. A kit of two AV500 adapters is <$100 and you can now buy them in speeds up to AV2000 although just like wireless the bigger numbers often amount to bigger lies.

If you depend on this connection.. and own the house get it wired with ethernet professionally. It is expensive but will fix the problem forever.

Wireless repeater setup should be last on the list.. it could improve the situation somewhat.. but could also cause other issues to the network.

IMHO I would buy Extreme and look at other options for backup. The Time Capsule is well overpriced now. A new extreme and with powerline to the second room.. and connect the TC in there with ethernet would perhaps work better.. but you can swap stuff around as you need it.

OR

I would buy a completely different brand of wireless router.. eg Asus high end models support Time Machine to a USB drive plugged into them.. I cannot say it is hugely reliable.. but neither is the TC now on Sierra and High Sierra.

I do not quite understand your sentence.. but if the current TC is over 3 years old and starting to have overheat issues it will definitely get worse. So you may not even be able to use it in a few months.

It might be a simple problem with the fan being blocked with dust and you can clean it out.. but the AC model airports are difficult to disassemble and easy to damage. Apple will not repair them. If it is less than 3 years they may replace it if you have applecare on a qualifying product.. ie computer, ipad or apple TV.