Summoning cured

[Fenster]

So i was playing an izzet deck against my friend with his black discard deck. We were both topdecking and he had a {Shrieking affliction} and a countered up {Quest for the nhili stone}.
Needles to say he drew a {Apetite for brains} and made me exile my last card. ({Niv mizzet, dracogenius}.) *Sigh* But on my turn before him i played a {Mercurial chemister} and i claimed that i could tap him (i had the mana) and draw 2 cards on my uppkeep after his enchantments had gone on the stack.
Now this i a series of questions.
First: Can i do this or is the chemister still sick to his gut?
Second: Even if i can do the enchantments check for hand size when they go on the stack or when they resolve? (I claimed the latter.)
Third: Does the summonning sickness end at begining of turn or at the uppkeep or end of upkeep?

My friend trusted me and let it happen but Im going to own up to it if i was wrong.
I eventually killed myself by casting {thoughtflare} without thinking when he had 3 {Megrim} out... Such is the life of a sleepy planeswalker.

[adventus]

Summoning sickness ends at the beginning of your turn.

302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.

[adventus]

First: Can i do this or is the chemister still sick to his gut?
Second: Even if i can do the enchantments check for hand size when they go on the stack or when they resolve? (I claimed the latter.)
Third: Does the summonning sickness end at begining of turn or at the uppkeep or end

First:  Yes, you can do this

Second:  Yes, when it resolves so you can use the creature's draw ability in response to the triggered ability, draw 2 cards, then the triggered ability resolves and you don't lose any life.  You could just use the chemister's ability during your untap step and avoid these timing issues entirely.

Third:  Ends at the beginning of your turn

[Fenster]

Thanks, man!

[KulrathKnight]

First: Can i do this or is the chemister still sick to his gut?
Second: Even if i can do the enchantments check for hand size when they go on the stack or when they resolve? (I claimed the latter.)
Third: Does the summonning sickness end at begining of turn or at the uppkeep or end

First:  Yes, you can do this

Second:  Yes, when it resolves so you can use the creature's draw ability in response to the triggered ability, draw 2 cards, then the triggered ability resolves and you don't lose any life.  You could just use the chemister's ability during your untap step and avoid these timing issues entirely.

Third:  Ends at the beginning of your turn

502.3. No player receives priority during the untap step, so no spells can be cast or resolve and no abilities can be activated or resolve. Any ability that triggers during this step will be held until the next time a player would receive priority, which is usually during the upkeep step. (See rule 503, "Upkeep Step.")

No one can cast spells or activate activated abilities during the untap step. Just wanted to clarify.