There is a step or two missing here - between the players describing what they want their PCs to do and the GM narrating the results of the adventurers' actions, we need to (i) work out what actions the adventurers take, and (ii) work out what the results of those actions are.
Working out what actions the adventurers take happens before step 2. The player works those out and then describes them to the DM. It happens in-between step 1, the DM description of the environment and step 2. Working out the results of those actions just means the details, like is the action automatic fail/succeed, or does it require a roll. That doesn't mean the action has occurred in the fiction, but instead is just informative to the DM and allows the DM to narrate the results. I suppose it is a step 3a for the DM to work out what the results will be before he narrates them and causes them to occur within the fiction.
Step (ii) is more than just the GM makes it up. 5e D&D has dozens of pages of action resolution mechanics.
Sure, but so what. I didn't say the DM makes up whatever he wants, though he is within his power to do so, he probably will use the mechanics provided to figure it out. It doesn't matter at all to my argument, though. The action doesn't actually happen within the fiction until the DM narrates it during step 3.
Step (i) is also more than just the GM decides. For instance, the combat rules only make sense on the assumption that a player's declaration of an attack brings it about (absent some defeating condition) that his/her PC is making an attack.
Step 1 isn't for the DM at all, unless the PC is trying an action that is outside the scope of the rules and he has to make a ruling on whether or not it is possible.
I don't agree with your claim, and if this was really true - that all a player of 5e can do is suggest to the GM that the fiction involving his/her PC changes in a certain way - then it would be one of the crappier RPGs ever published.
It's the way the game is written. Bring it up with the designers if you don't like it.
Even in your example, who is it who decides that the fiction includes Olaf jumping, attempting to clear the stream? It is the player.
Of course it's the player. Unless there's some sort of mind control magic going on, the DM isn't going to be doing that for the player.
The duration of the spell Magic Missile is listed as Instantaneous. I don't think it takes 6 seconds for the missile to fly from the caster to the target - that does not seem very instantaneous to me.
So is a Fireball, but the description describes the streak of fire moving. All instantaneous means is that the duration doesn't go from round to round, not that the effect takes place at the speed of light. During that travel time, the Magic Missile is vulnerable to the Shield spell. Once it hits, the Shield is useless.
As far as a Shield spell taking only "a fraction of a second", that is not written anywhere in the rules.
If by not written anywhere in the rules, you mean written on page 202 of the PHB under Castin Time - Reactions, then I agree with you.
"Reactions
Some spells can be cast as reactions.
These spells take a fraction of a second to bring about and are cast in response to some event."
The rules for reactions (Basic PDF, p 70) say that "A reaction is an instant response to a trigger of some kind." That suggests that a reaction takes about the same time as the missiles take to fly from the caster to the target. (And this makes sense in a more general way - eg there's no reason to think that stabbing an orc as a reaction is significantly quicker than stabbing an orc as an action.)
Perhaps you should invest in a PHB instead of relying on the Basic PDF.