First pair: You can do U L2 u L2 u' L2 instead. It's really faster. Some people say it's bad for look-ahead. Your choice.
Second pair: You see that for your pair you had to rotate. Instead, solve red-blue first; the red-blue edge is oriented, hence you don't need to rotate. For example U2 R' U R U' R' U R. After that you can orient the remaining two F2L edges by just y' and solve everything <R,U>. Also you did U2 + U for your pair, that can be a U' instead. You don't even have to do a U move at all and just insert by y' R U2 R'. Another important aspect is that after second pair you end up with your two front slots solved, so you did a y2 to be able to see pieces on the back. y2 should be avoided, it costs too much time. So instead of inserting with y' U R U' R' you should do y U L U' L'.
Third pair: As mentioned above, the y2 is avoidable, although it's rather a mistake on second slot. You saw the green-red edge stuck in the FR slot and instantly took it out by U' R U2 R'. The pair ended up not being paired. Instead, try to bring the edge up and set up the pair at the same time, for example: R U R' U', then insert by y' R U R'. Admittedly that gets the next F2L edge stuck in an awkward way in the last slot but at least it's much shorter. An alternate solution preventing that would be y R' U R to set up the pair. Now you could just normally insert and get an okish F2L case for the last pair, or (slightly more advanced) you insert the pair by doing a hedgeslammer (F R' F' R) to keep the blue-red edge oriented, then F2L-4 can be solved just by U2 R' U' R.
