yes,

yes,

yes,

and yes.

ok, basicly, if culture is enveloping your planet, your allegiance climbes to +10% of what it would have been normally. THis means, for your homeworld, your allegiance goes up to 110%... or you get a 10% boost on extractor and tax income... now, for a planet far from home, the allegiance change is from 25 to 35%... which means a relitive 40% increase on your extractor and tax income! (aka, broadcast centers are more important for large empires than small ones.

here is a quick calculation of the respective boosts on extractor and tax income for your planets.... allure of unity, and advent starbases change this, but its the same for vasari and tec.

HW- 10%

1 hop- 11.1%

2 hops- 12.5%

3 hops 14.3%

4 hops 18.2%

5 hops 25%

6 hops or more (or no hw) 40%

culture ALSO (after appropriate research) gives combat bonuses... antimatter regen for TEC, shield mitigation for advent, and damage bonus for VAS. see the appropriate research for the quantity of those bonuses.

that should answer questions one and two.

yes, having enemy culture can have negitive effects. The advent can see planets where thier culture is dominating, and the TEC can severly reduce production rates on planets where they are dominating. (I was playing a game... and it took twice as long to build a colony ship thanks to tec culture than it would have normally) Vasari culture has no negitive effects, (beyond that they get thier damage bonus) ALSO, enemy culture surrounding your planet means that its allegiance is decreasining... so LONG before you lose your planet you will be losing significant quantities of tax and extractor income.  If you manage to save your planet at 1% allegiance... and get it to stop losing allegiance... your still losing 99% of that planets income,

4 has preety much already been answered, take a look at the different race's tech trees to get a better understanding of the differencs.

And the Advent Deliverence Engine also gives a 25% damage bonus (15% in basic sins) to allied ships at the target planet, though this isn't directly linked to culture.

Also note that pretty much all effects of culture besides the allegiance change must be researched first. (like slow production and vision)

Oh, and Starbases repel culture too, so if you have the economy you can send your capitals somewhere else and put a SB at the contested planet to push away the enemy culture (which might be a good idea anyway, as a big red button will deter "normal" invasions more effectively than a Kol or two)

In entrenchment, starbases dont repel culture.

You can spread culture by simply waiting for the culture line to spread to that planet. You can speed it up by building more broadcast centers, or by researching more broadcast strength.

This is correct...who ever was under the impression that starbases repel culture probably was looking at an advent starbase with culture...any other situation, and the starbase says culture repel rate is 0, so unless its hidden somewhere in the game mechanics SBs don't repel culture...

Well, first off, did it get hit by a deliverance engine?  If you are playing against the AI, this is HIGHLY unlikely, but I suppose possible...if this is the case, that culture loss will only be temporary, so no worries...

More likely the enemy just has a lot of culture on your HW...there are three things you can do about this...one, bring your capital ship(s) to your HW, caps help to resist enemy culture....two, build more culture facilities, which might suck if you have to scuttle things, but you may not have a choice...three, research culture techs...this may take a while but it is a much better long term solution...

A thing to keep in mind...culture kind of has a delay...you don't see the effects of culture until a little while after the broadcast centers are built, so whatever you do, remember the effect might not be instantaneous...don't assume something doesn't work just because that -.07% isn't instantly changed, culture takes time to work...

If you have the fleet for it, you can also attack a neighboring enemy world and destroy their culture facilities...thats the root of the problem, and it will buy you time...

Yes