An mBTC, or MilliBitcoin, is equivalent to 0.001BTC" is this a fixed "forever" exchange rate (BTC)1:1000(mBTC)?
This is not an exchange rate, it is just a unit prefix. There are 1000 millibitcoin in a bitcoin, in the same way there are 1000 millimetres in a meter. Some wallets will allow the user to change the unit that their balance is displayed in (eg BTC, mBTC, sats, etc). Functionally, there is no difference between BTC and mBTC, it is just a display preference.
and it complains "not enough funds" for transfer.
The bitcoin network has been extremely busy for the last few days, so transaction fees are currently very high compared to the what we've seen for the last year. Your wallet may be attempting to construct a transaction which includes a very high fee (more than the wallet contains - which seems kinda crazy, but I've seen some very poorly designed fee management algorithms in some wallets before), but without additional information, its not really possible to fully diagnose the issue. It is probably worth contacting the developer of the wallet if the problem persists. You can also search for 'mempool visualizer' online to watch how busy the network is, and then make transactions during less busy times.
Keep in mind as well, some scam wallets will ask you to deposit coins in order to 'unlock a deposit', 'pay a transaction fee', or some other similar nonsense. I am not saying that the wallet you are using is indeed a scam, but I have not heard of it before, so I mention this just to make you aware of the possibility. The prudent bitcoin user stays alert for such scams.
Schildbach Wallet (...) this app was shown to me by a friend.
I̶ ̶h̶a̶v̶e̶ ̶n̶e̶v̶e̶r̶ ̶h̶e̶a̶r̶d̶ ̶o̶f̶ ̶t̶h̶e̶ ̶w̶a̶l̶l̶e̶t̶ ̶s̶o̶f̶t̶w̶a̶r̶e̶ ̶y̶o̶u̶ ̶a̶r̶e̶ ̶u̶s̶i̶n̶g̶ (EDIT: this wallet is indeed listed on bitcoin.org, as RedGrittyBrick pointed out in a comment below). To help ensure you are using software which is not malicious, I would suggest starting from this page: https://bitcoin.org/en/choose-your-wallet. There are a lot of malicious wallets out there that will steal/scam you.
how in the world, should this be usable to buy a cappuccino worth 3.10€?
When the network is busy and fees are high, it really isn't. During low fee times it is more reasonable, though it is worth mentioning that a ledger which computes and stores every person's coffee transaction information for all time (on tens of thousands of nodes) is a grossly inefficient way to expect a monetary network to work.
If I had to make a small value purchase using BTC, I would instead use the lightning network, which is quite well suited to the job. Doing so will generally require setting up a lightning node/wallet before transaction fees skyrocket though.