野球監督 is a baseball coach, i would definitely translate 監督 as coach for the entire thing. director doesn't really make sense in this context.
the only problem i see is really that the movie director joke late in the episode suffers a bit, but i really wouldnt sacrifice the proper translation for that.
00:00:44 future instead of 'fute'
Ikoma stuff at 0:01:45 - so i think she's saying that ikoma's kennin ended and therefore she wants to change her name to a different idol - 'just change my role already' maybe? - your guesslation line could made to something like 'but you fit ikoma perfectly' to make it more clear
i would capitalize Tradri
0:03:20.28 - she might be saying raburii, lovely instead of double? really not sure, you might be right
0:04:13.81 - i would make this ['Coach', huh...?] - i'll just put my suggested lines in [] from now on
0:04:16.96 - [Do you know something about it?] - ikuta isn't sure wether or not they actually do
0:04:18.72 - [We will never forget!]
0:05:19.22 - Athletes instead of athlete i think
0:06:46.18 - [Teach us Softball, please!] - grammar was a little off
0:07:25.15 - [Sorry for bothering you...]
0:09:41.38 - [You used to be a coach, right?]
0:10:16.79 - typo
0:10:19.55 - no clue either - 'tsuretekita ... dore ...' is what i could make out?
0:10:34.42 - [It's not just gonna work out like in a comic, huh...] manga or comic is up to you i guess
0:10:37.34 - typo
0:10:40.59 - [I used the Fermi function to calculate the probability of beating Polaris Academy without a coach.]
next line  - [The result is 0.000000000000-]
0:10:55.79 - 'teach' instead of 'show'
0:11:19.01 - i think that line is correct, i guess the joke is supposed to be that she starts rambling about the whereabouts of random people that weren't asked for?
0:11:52.83 - punctuation
0:12:14.92 - i think it'd be funnier if your comment only showed for two or three seconds instead of the entire scene
0:14:31.06 - [It's impossible after all...]
0:17:04.69 - 'nazu ni okay?' is what i'm hearing. don't get it either though.
0:17:05.84 - 'nanka wakanai kedo, douyatte shikkakushita mono' is what i'm hearing. don't get it either though.
0:17:38.14 - [Still more?]

this is what i got so far, it's already morning and i'm tired as fuck, gonna look at the rest tomorrow. i'm also gonna keep thinking about the 'unidentfied' lines for a bit.