during my session the following hand came up and i wasn't sure how to play it. i pushed all-in, but i felt it was probably wrong. so i marked it to analyze it after the session.
here is the hand how it was played:

PokerStars No-Limit Hold'em, $1.00 BB (7 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com
saw flop | saw showdown

Button ($105.80)
SB ($59.25)
BB ($117.95)
Hero (UTG) ($140.15)
MP1 ($115.10)
MP2 ($100)
CO ($109.60)

Preflop: Hero is UTG with 8, 5
Hero bets $3, 1 fold, MP2 calls $3, 2 folds, SB calls $2.50, 1 fold

Flop: ($10) 9, 4, A (3 players)
SB checks, Hero bets $6, 1 fold, SB raises to $18, Hero raises to $137.15 (All-In), SB calls $38.25 (All-In)

Turn: ($122.50) 10 (2 players, 2 all-in)

River: ($122.50) A (2 players, 2 all-in)

Total pot: $122.50 | Rake: $3
Results:
SB had 9, A (full house, Aces over nines).
Hero had 8, 5 (one pair, Aces).
Outcome: SB won $119.50


now i am not sure if my post-analysis is right. my thoughts about it:

1. how the hand was played:
i think my preflop raise (i mix some sc and suited 1/2gapers in my ep range) and flop c-bet is standard.
then i got raised from the sb (23/8/1.1 over 80 hands).
first i calculated my equity with pokerstove. i gave him AT+;two pairs;sets and some flush draws. my equity against his range is about 35%.
i have 35% or 1.9:1. but my odds when going all-in are about 72:50 or 1.4:1. so i am not getting the right odds to play.
but it could still be profitable if i have enough fold-equity through the all-in. but in that case i guess i have almsot no fold-equity. he his 59bb deep when the hand started and committed a total of 21bb when he raised the flop on an ace high board. so i have to assume he will fold almost never here.
so i played the hand wrong.

2. how the hand is played right:
on the flop i have three choices. raise was wrong. so i still have call and fold.

2a. call:
the pot odds for a call are 2.8:1. my odds for hitting the flush on the turn are 4.1:1, so it's not enough for a call based on pot odds. so i have to look for the implied odds. when i assume i get his whole stack if i hit a diamond on the turn i get 72:12 or 6:1 odds. since i think he is willing to commit his whole stack on the turn i have enough odds to call.
so a call on the flop would be the right play (assuming i will get his whole stack after the flush arrives).
with a diamond on the turn i would push all-in. with a non diamond on the turn i would check-behind or fold if he bets.

2b. fold:
fold would be the right play if i think he would not commit the rest of his stack when a diamond comes on the turn. so if i would not get enough implied odds i have to fold.


is my analysis right here? if not, where is a mistake?
please give me your thoughts about my analysis.

Fold preflop AINEC. Balancing (especially at 100NL) isn't a good reason to raise this hand. You will not be able to play it profitably OOP.

I skimmed your analysis, and it seems off because you don't account for him having a higher flush draw or a set. I think the flop is a fold, despite this board being in the top 15% of boards for our hand. Just goes to show you again why preflop is a turbo fold.

Fold pre. your range is balanced if you play some small pocket pairs and ocasionally a good suited connector.
Flop. You clearly represent an Ace and get reraised on the flop. Not a good spot for him to bluff. He should also not reraise with a flush draw (unless he has some extra outs), especially since he has position.
So his range consists mostly of strong made hands like AK or a set, and maybe something like t9d.
Against that range you might call. You have position and a disguised hand. But folding is good as well. A shove is a big error.

may i suggest 87 suited instead.

This.

Flop is a clear fold because we don't have the NFD.