Is it okay to chain and broadcast multiple unconfirmed transactions?  

For example: I have two confirmed UTXOs `UC1` and `UC2`. Using both as inputs, I then create and broadcast transaction `T1`, which outputs `UT1`. Then, using `UT1` and another confirmed UTXO, `UC3`, I create and broadcast `T2`, which outputs `UT2`. I keep track of the last unconfirmed UTXO from the transactions I built and keep building and broadcasting new ones.

Secondly, will the chained transactions be mined at the same block?