Sorry, I don't think any of us have really answered fully the questions you had. The main issues are, as I said earlier, that you will have to check in and get boarding passes separately for each ticket. That is always the case, unless you happen to be booked on the same airline all the way through, in which case some airlines allow you to get all your BPs at once (UA does this).

You should budget time between flights to collect and recheck your bags if you are unable to check them all the way through across separate tickets (this is not usually a problem, but as I said some airlines do not allow you to check bags through onto separate airlines, or you may just run into an unskilled check-in agent).

You should also budget time between flights to accommodate any delays that can occur. If you are flying on a single ticket, the issuing airline "protects" you from getting you lost en route in the event of a misconnection. For example, on a single ticket, if your UA flight is late and you miss your connection to the TG flight, you are still "protected" and UA essentially offers a guarantee to get you to your final destination in the event of such mishaps.

On two separate tickets, you are not protected. To many airlines, and on flexible tickets, this doesn't matter much if you're a little late showing up for your flight (things happen...they know this). However, it is entirely possible that if one flight is late and causes you to miss your connection, you may have to pay a change penalty, or lose your entire booking. It's a small risk, but it's there. Slightly O/T, but LCC's are particularly unsympathetic in this regard.