When a character is surprised, they can't move or take actions (including bonus actions) on their first turn, and they can't use a reaction until the end of their first turn.
Well and good.
But can a surprised character still do all those other things listed as "other activities on your turn"? Can they communicate with 'utterances and gestures', interact with objects, and so on? Can they, for example, draw weapons and shout 'help help!', or ring a bell they have in-hand?
In context: The rogue and warlock, who are both very stealthy, try to ambush a couple of guards and "take them out commando-style" before they can raise the alarm. Apparently, in order to do this, they have to not only gain surprise (not a problem), but also roll high enough initiative that they can attack before the guards get their first turn (risky) during which the guards can only, apparently, shout for help and ring their alarm bells. But if it's just about who gets the top initiative slots, what's the difference between using all that stealth, and having the whole party just charge right in and hope two of them roll a high enough initiative to take both guards out before they can react?