If I'm level 29, does that mean that all of my fully powered up Pokémon will also be level 29?
No. If fully powered up, at Level 29 they will be Level 30.5 (all Pokemon fully powered up are always 1.5 levels higher than your level; they go up in half level increments).
Once I get past level 30 how can I tell when the Pokémon are at level 30?
The easiest way is to use PokeGenie; put in a screenshot and it will tell you your Pokemons level.
The other way, is at Level 29, the cost to go up increases to 5,000 dust per increment, so if you level up twice after the cost reaches 5,000, it'll be level 30.
Also, you know when it pops up saying +40/+50 etc when you power up? Anything after Level 30 will be powered up half what it was before (so if it was +40, it would now be +20). Hence why I don't power anything up after it hits Level 30 
Will I start needing loads more stardust to power them up?
Not immediately; it carries on going up gradually as it always has before. After 31, for example, it increases from 5,000 to 6,000.
Anybody know if there will be any events soon with double of stuff. I know we had doubly candies for Halloween last year.
Nothing has been announced. Legendary birds are until 31st August and then Mewtwo is expected to come soon after in Exclusive Raid Battles (that you need to be invited to), so nothing on the immediate horizon.