Safety, basics: How do I store and save my transactions?

I just started using bisq (and crypto in general). I transfered some bitcoins from another account, and I also bought some directly to bisq from my national currency (with a local/national) phone-application.
Anyhow, now I am concerned that the information about the transactions will be kept intact allright, and thus the value kept safe. Should I push the button “Backup” to be sure to save everything? Where is it being backed-up then?

Second noob question:
So far I thus sent bitcoins to my Bisq, but now I want to buy Dash for my BTCs.
In order to do so it seems I need to add a trading account with my BTCs. How do I do that - I cannot figure it out. Does it have anything to do with the BTC’s “Address - Recieved with”-heading or with the “Transaction ID”-heading?

Well your bitcoins are always safe as long as you have your wallet or seed words. Bitcoin transactions are always on the Bitcoin blockchain, so they can always be recovered, you don’t need to store them yourself as the whole Bitcoin network is storing them. But if you want, you can still just do a backup as you mentioned. When you go to Accounts->Backup you can see the backup button and the location of the backup above it.

In order to trade any altcoin, including Dash, only thing you need now is to create an altcoin account in the Accounts. There you will specify the Dash address to which your coins will be sent to.