Flying to Amsterdam from London

Yes you will go through passport control/immigration (this is where they stamp your passport and ask you purpose of visit type question) and then you exit through customs in the baggage claim area. Customs is after baggage claim.

Note that current rules might change when/if the UK leaves the EU, so it might be very different in April. (You can also take the train, cheaper and more comfortable than flying.)

You may want to consider taking the Eurostar train to Amsterdam, which will be less hassle. There will still be border and security checks, as the U.K. is not in the Schengen Zone.

Yes. UK is not part of Schengen immigration area—so in the Netherlands you will go through passport and customs control. I suggest however going from London City airport to AMS. Much easier to pass through on both sides.