1. What is the difference between a bitcoin wallet on your smart phone (androind or app store) like bitcoin.com app versus an exchange like coinbase or bitstamp for example??
Those wallets that are in your smartphone or in your web browser are called "hot wallets." They are vulnerable because of viruses and hacking. If you click on a wrong link or something, someone may get access to your computer/smartphone and take all your assets.
Having your money in an exchange also have its cons. They can get hacked themselves, you can potentially get frozen out of your account, etc. Also some exchanges(like Robinhood) do not even let you take our your assets - instead they are holding the assets in your name. You don't actually own it.
The most secure way of storing your crypto is in what's called a "hardware wallet" or "cold storage." i.e. Nano Ledger, Trezor, etc. You alone have the "keys" to your account and only when you physically plug in your USB and enter the password (Nano Ledger, Trezor, etc) can someone take assets out of your account.
2. Is it safe to keep your bitcoin in an wallet app like bitcoin.com?
Safest way is cold storage/hardware wallet.
3. How long can a Trezor last for, will the battery die after 5 years then you are screwed?
Whenever you set up a hardware wallet like Trezor, they make you write down a randomized 24 word seed phrase. This is written down on a piece of paper which you will put someplace safe like a physical safe or safety deposit box or under your mattress (although I don't suggest that.)
If you lose your hardware wallet, it goes bad, it breaks, etc. All you need to do is buy another one and recover your old account with the original 24 word seed phrase.
I personally do not like the Trezor because of one thing I see as a flaw. When you input the 24 word seed phrase, you type it in on your computer as the Trezor is connected to your comp. That's a flaw IMO because if someone hacked your comp, they may be able to see what you type with a keylogger program. With that, they can steal everything you have.
On a Nano Ledger, you have to physically type in the seed phrase on the device itself. So the person would need physical access to your actual wallet to do anything.
On top of that, the Ledger has the most coins it supports over the other hardware wallets.