Holding top pair and flush draw: call a 4-bet shove on the flop?

You played your hand as if you had the nut FD. Just call the raise and re-evaluate the turn.
Noone here will like your idea for limping. You should never limp. Your hand is perfect for an iso raise preflop. You try to isolate yourself with the limper and do not give opportunity to the players behind you to iso raise both limpers.
If you are up vs a set what exactly are your 11 outs?

Thanks for the reply. I'm afraid that (as you're probably implying) I'm overcounting my outs, because I'm counting Q♥ and Q♠, when these will always give villain a full house if he has a set.

Let's think about V's range a bit. If he's playing exactly the BBS as set out elsewhere on this site, then his pre-flop range is {JJ-22}. It's probably not too much broader than that, because at 19/15 he isn't calling a lot. Then his post flop range is only {JJ, 33}. That being the case, I basically need to complete my flush to win. There's no point raising here, because V will never fold his set. So I ought to decide whether to call depending on the odds offered. I need $0.31 to call his raise and there is $1.31 in the pot, so the pot odds offered are 4.2:1. Those are actually the exact odds I need, so I don't lose by calling here even if I can't get any more money on the following streets (I have 9 clean outs, since none of 2, 4, 5, 6, 7, 8, 9, T or A of clubs will improve his hand). However, because his hand is strong, it's very likely that I will get more if I hit on the turn, perhaps even as much as his whole stack. So call is excellent value here. From which we learn that his raise is much too small.

(If I call and a club does come on the turn, he will have 9 outs for FH or quads (only 9 because I have Q♣ ). So I would then need to raise by a sufficient amount to give him incorrect pot odds. He's not getting any implied odds, because I see whether the board pairs on the river or not. So in theory a half-pot raise on the turn would be sufficient in this scenario. However, I think I would raise 2/3 pot, because I doubt it makes any difference to his next action, which as likely as not will be reraise all-in. (The hypothetical line is that the pot is $1.62 at the turn, I bet $1.08, he has $3.07 left in his stack, there's no sensible raise which doesn't leave him pot-committed, from his perspective he's either ahead and needs to protect or he's behind but has 10 outs. Cf example 26 on this page.) So the actual analysis is that I have an 80% chance of losing $0.31 (36 of the remaining 45 cards are non-clubs, in which case I x/f the turn), a 4% chance of losing $3.38 (turn is a club, we go all-in, he hits the river) and a 16% chance of winning $4.38 (the money already in the pot plus the rest of his stack if the turn is a club, we go all-in, he misses the river). So EV of calling is +$0.32.)

So I think call is definitely correct here. However, I'm not sure that I take your point that I don't have the nut flush. The only way he can have a draw for the nut flush is if he cold-called pre-flop with Ax:club:, where x is 2, 4, 5, 6, 7, 8, 9 or T, from MP, over my raise from EP. With a profile of 19/15, I can't see that ever happening. He might have A♣Q♠ or A♣Q♥ for a BDFD I suppose. In that case the analysis would be much the same as above, except now when I complete he has 7 outs for a higher flush instead of 9 outs for a FH/quads. If I did put Ax:club: in his range, I think I would have to fold here, because I lose $3.38 when I hit my flush on the turn if he has these cards (or if I'm not betting when I hit my flush, my call would be pointless).

Why do you think he holds only PPs? His range will be more like 77-QQ, AJs+,AQo+ pre-flop. KQs, may be. I do not know whether he will have some SCs but the only reasonable one, raising that flop is Tc9c.

His range is {JJ-22} if he plays exactly according to this article. I admit that's a bit unlikely, but it's not totally far-fetched given that he's playing NL4 and showing a reasonable profile. If your range was correct, his post flop range would be {QQ, JJ, AQ}. That would make call less good (and raise better). As I noted, the 2 AQ combos with A♣ play much the same as the sets. The other 6 AQ combos he may not bet again if a club comes on the turn, but he may bet once more, and he has no chance of catching me, so I have EV about +$0.12 for the call (on the assumption that if a club comes and I raise, he calls 50% of the time and folds 50% of the time having TPTK and no draw), which gives me an EV of some +$0.19 for the call overall.

The actual line I took may be better here, because I would expect the 8 AQ combos to fold to my reraise, whereas we know (now) the 4 combos in {QQ, JJ} go all-in (at which point fold and call are equivalent, from it which it follows that I've just lost the value of my reraise). So I have 2/3 chance of winning $1.31 and 1/3 chance of losing $0.96, which is EV +$0.55.

These articles might have been correct when they were written back in 2010, but the games have evolved so much since then, so you can't really use them too much these days.

His CC range should probably look more like QQ-77, ATs+, KTs+, QJs, JTs, T9s.

I think we should just call his 2b, call turn and give up when we miss the river.