kolsch/alt beer question

Alright, Ive got my kegs full of big beers and need some lighter stuff for summer. thinking about doing a double brew day of BIAB 3 gallon batches of Kolsch and an Alt beer (both styles Ive never done).

The recipes I have call for 2 week primaries at 60 and then a month lager period at 34-35. During the lager, is it a requirement that I pull the beer off the trub (therefore requiring a secondary)? The thing is I only have one 3 gallon Carboy and If I cant lager without a secondary Ill probably just brew one. I dont want to really tie up my ferm chamber for a month on one beer though.

you can lager in the primary. I wouldn't lager it for 6 months in the primary, but 1 month shouldn't hurt.

Is this because the lagering stops the fermentation and trub activity (therefore eliminating off-flavors that would appear in an over-primaried ale), or is that incorrect?

Assuming you're using Kolsch or Alt ale yeast then you will be essentially cold crashing the yeast out of suspension once you put it in a 34 or 35 degree fridge or whatever. I make a dusseldorf alt frequently and I always "lager" in primary. Although with the ale yeast you really aren't lagering so much as just giving the beer time to drop out the yeast and clear/clean up.

I will say that lagering on the yeast cake can make it more difficult to siphon into the keg without pulling yeast and trub back into the beer. Because of this and because the yeast I used doesn't flocculate very well I typically will mix up some gelatin to add when I move the beer to the keg.

You can also always get a spare keg and transfer the beer to it after fermentation is complete then purge the keg and let the beer lager in there for a month.

Definitely make sure fermentation has sopped before lagering. If you are fermenting at 60. I'd say leave it at 60 for a month. Then lager in a seperate vessel if you want. I like to lager in kegs.

Nope. There is still yeast present even after moving off the primary yeast cake. If you are using a lager yeast they will still be active, at least a little. That helps clean up any byproducts of active fermentation. Ale yeasts, not so active at the 35ish temps, so make sure all fermentation, including cleanup, is complete before moving to cold temp.
'Lagering' just means storage. Usually at cold temps. The settling process at cold temps will help make a real clear beer.
I usually move my lagers to a carboy after 3 weeks or so, and store at 30-40 for 4-6 weeks, but I would be pretty sure that 1 month in the primary bucket at lager temps would be just fine. I've read posts where people are storing ales at ale temps in their primary for a couple months without off-flavors.

I was definitely planning on using kolsch and alt yeasts. I think my new plan is to put one into secondary and put one in a purged keg to lager. Ill just bottle the one coming out of secondary.

If this is only a 3G batch should there be any issue purging a 5g keg with co2 and leaving 2g of head space for the lager phase?