Answer depends on what kind of grass you have and what kind of weeds you have. The grass you should be able to answer but you might want to take pictures of the weeds. If you can take them when it is shady that is much better. The organic weed control is vinegar. Unfortunately it is non selective and will kill the grass, too.

Don't roll it. Rolling will tightly knit the surface, making the sod roots difficult to penetrate. You want the soil friable, not compacted. Spread your compost and mix it in during the grading with a rake. That's good enough. If you till, there are thousands of weed seeds you could be bringing to the surface but never get them to germinate on this attempt. Plus, there are other disadvantages to tilling. I don't exactly know what you mean by "thoroughly pre-irrigate" but make it about a week of shallow watering maybe twice a day. That's what weeds like, not saturation. Roundup is not persistent in the soil. You can lay your sod one week after spraying the weeds. The herbicide will get into the growth of any plant it touches, not anything the chemical does not touch. I don't know of a pre-m herbicide that controls germination of any weeds likely to grow this time of year. Pre-m only prevents weed seeds from germinating. Depending on which pre-m herbicide used, some will impede growth in early stages - shortly after germination. Just best not use it in this instance. Just food for thought, you risk of alienating and never benefiting from some very knowledgeable people when you exclude them like that. Think about also, there may be someone who has done it before but doesn't mean it's the right thing to do.

I'd say cinquefoil (Potentilla recta). Here is a link that might be useful: Cinquefoil Images

There's no crabgrass in your pictures, so don't get something specific to crabgrass...yet. That might be orchard grass or barnyard grass, but it isn't crabgrass. Crabgrass sprouts about now at the earliest and could not possibly be that tall. Besides that just doesn't look like crabgrass. Historically the advice on first fertilizer FOR BERMUDA is to apply after the second time you mow real grass, not weeds, in the spring. This is only for bermuda, because it can take it. It will speed up the normal spring flush of new growth, so get ready to mow 3x per week. The reason for not applying before the 2nd mowing is that the roots are not awake yet to take up the fertilizer. You would be wasting it. After 2 mowings the grass is fully awake. It doesn't look like the contractor rolled the sod down after laying it. Have the roots grown down into the soil? Can you lift any corners up? Is that a live oak tree in the front yard? If so the bermuda underneath will eventually die out as the tree grows up to provide lots of shade.