Not quite, here you can say "I still haven't found someone who I can play with." Or you can drop the who/whom completely and just say "I still haven't found someone I can play with." Though if you were to arrange the sentence differently you could say "I still haven't found someone with whom I can play with." Any of those three is a correct way of saying it, but most people will use the second one. "I still haven't found someone I can play with." Who/whom is a confusing one, even most native English speakers don't use them properly. We usually just use 'who' all the time but we aren't actually correct to. What do you mean by third conditional? I haven't heard of that before.

I think your first sentence is correct how it is, though to be completely honest most English speakers leave out the "whom" so that it just reads as "I still haven't found someone I can play with" or even "I still haven't found someone that I can play with" though the added "that" is technically incorrect. This website might help with who vs whom if that's what you're confused about: http://web.ku.edu/~edit/whom.html I'm not sure what you mean by your question about changing the "third conditional" to could have or should have. Could you elaborate? I hope this helps!

1. Yes, this is correct. You are right to use 'whom' here, because 'whom' is an object pronoun. However, it is the not most natural way for a native English speaker to phrase this idea. As Jason suggests, it would be more natural to miss out the pronoun entirely and say 'I still haven't found someone I can play with' or even 'I still haven't found someone to play with.' 2. Yes, you can use 'could have' in a third conditional. For example: 'If I'd left the house two minutes earlier, I could have caught the train.' 'Should have' is mainly used to talk about a regret in the past, something which was supposed to have happened ,or would have been better if it hadn't happened. For example: 'You shouldn't have spent so much money on my present! It really wasn't necessary.'

That"s what I thought. Thank you Kenny :)

I still haven't found someone whom I can play with. Correct > Who can't you play with ? Test reply > I cannot play with him / her/ someone. If the anwer is this -- not "HE" , "she", etc ; then you are correct . ""Whom" points to the object of the verb -- the person you cannot play with. Example > Whom did you called ? I called HIM > then it's correct / Or the object "recieving" the verb "called" I saw you with a person who I think is a crook . Test reply> Who looks like a crook? HE looks like a crook > Then "who " is correct .