- An axis engineer setting mines around fuel dump from start.
I think this depends on the ally team you are facing. If they have a Covert Ops who is worth their salt, then yes, get the fuel depot mined,
especially the front door and the door to the top. Its far too easy for a CovOp to get a uniform and slip into the fuel depot and once the CovOp is in, it only takes one slippery engineer to make a good bridge defense moot. Usually, I will try and spawn back at the Fuel Depot spawn point as an engieer early on, if my team looks like it will hold the bridge for a bit without me, and set up mines and the gates. I’m not that important that my team can’t get along without me for a while.
- An axis engineer to build first tank barrier from start.
This is something I would always suggest. That first tank barrier can be a killing ground if the axis are halfway competent. With it being so close to the axis spawn, and with the barrier as exposed as it is, it can be a real pain for an allied engineers to plant on it, and defend the dynamyte long enough for it to blow. Though as Dawnrazor pointed out, it needs to be only one engineer doing this, everyone else should protect the tank. That is the first choke point, and a damn good one.
- An ally engineer to destroy first tank barrier before tank is actually repaired.
Hadn’t considered this one before, I guess it would be ok if it is only one engineer again. But, considering the difficulty that can be had in getting the tank repaired, the allies probably need all the help they can get in getting the tank up and running. Plus, this might just create another tug of war, blowing up the barrier, axis rebuilding it, which would chew up resources and time that the allies don’t have. On the other hand, that barrier can be a real pain to get past once the tank is moving, so maybe one engineer to keep it down would be well spent.
- An ally engineer planting mines in front of second axis spawn in gold rush, to kill some after tank is taken.
This is just good clean fun. 
- Someone to block entry through axis spawn in gold rush, as soon as doors are open.
This is almost a requirement for the allies. With the axis spawn so close to the bank, the allies need to do something to stem the flow of axis soldiers into the vault. Mind you, I would at least say stay outside of the actual spawn area, but once they get to the tank/first archway, I say the axis soldiers are fair game.
I mean, do you think it’s good to send a small part of your team to “next” objective weakening a little “current” objective. It helps recovering from a first objective loss, but could also be the reason of it.
This is probably going to be a judgement call each game. If you have a team that can probably do without you for a little while, then sure hit the next objective, just keep in mind that means that your team is down a man, and the other team may well be able to just rebuild/recover from your getting ahead while your team is still stuck at the previous objective. For example, my personal pet peeve are the engineers who are blowing truck barriers and/or repairing the truck before the bank doors are even blown. The truck and associated barrier can wait until the gold is in the truck, until then, get down to the courtyard and help your team.