"Weed" seeds are brought in to any lawn via birds and wind so there is no way to prevent them from moving in that is economically viable.
If the seam edges are drying then they were not properly laid. What I have done to correct this is to cover those seams with a good soil mix. We have a garden center here where they mix a close approximation of loam, 45 percent sand, 25 percent silt, 25 percent clay, and 5 percent organic matter.
If the soil this sod was laid on was properly prepared before the sod was laid then "fertilizing" should not be necessary. Feeding the soil should be done regularly however, such as mulch mowing the grass clippings which can provide up to half the Nitrogen needs of the lawn each year and, if available, mulch mowing deciduous leaves into the soil. The idea that spreading some kind of "fertilizer" monthly, or 4 times a year, comes from the synthetic fertilizer industry that must do that to keep the drugged lawns looking good.
Initially, watering often is necessary until the sod gets established. How much depends on a number of factors starting with your weather. During cool, moist times your lawn will need less water then during hot, dry times. Roughly most lawns will need about 1 inch of water per week, whether from what falls from the sky or what you apply via a sprinkling system. But, during hot and dry times that same lawn may need more water, because of draiange and evaporation. All plants lose more water when it is hot and dry than when it is cool and moist. You need to pay attention to the lawn and not rely on a "schedule" for watering.
How high to mow depends on the type of grass you have. As a rule, the more blade exposed to the sun the better for the plant since that means the plant can manufacture more nutrients via photosynthesis. The healthier a lawn is the more grass blades it will produce making for a denser lawn that makes it harder for unwanted plant growth ("weeds") to appear. Warm season grasses seem to do best if mowed 2 inches or so while cool season grasses do better at 3 or 4 inches.

You might have read something I wrote about my experiment with monthly feeding. I was trying to see if there would be any harm come to my grass from overfeeding. There wasn't. You don't need to fertilize nearly that often unless you have good reason. Once in late spring (Memorial Day), once in late summer (Labor Day), and once at Thanksgiving should be enough. If you want to get slightly more crazy, hit it again at 4th of July. You can use any of the fertilizers you listed. I never mix them unless I simply have some left over.

Sac'to (and I know y'all hate that as much as I hate San Antone) is no different than other places regarding watering. You would have to get into the sandy lower desert of SoCal to find exceptions to deep and infrequent. Watch your grass and let it tell you when to water. Measure your sprinkler output using tuna or cat food cans. Some systems can put out a full inch in 20 minutes. Mine takes 8 hours. This time of year if your grass dries out in less than 7 days, water immediately and water deeper. Keep an eye on your wind. As long as you have a sea breeze there is some moisture. That moisture drops out fast as you move up in elevation to the east. But any time you have wind from any other direction, consider it to be dry and watch your lawn more closely for signs of drying. In the fall you will see the lawn is in pretty good shape even after a week. Then you can start to stretch out the weekly watering to 10 days and then two weeks. Eventually it will be monthly from Nov thru April.

I just replied to your nutgrass post and asked where you live. You don't necessarily need to reply to that as I got the rest of the story here. Nobody here knows that SZ means Sunset Zone and nobody knows what those zones are. Besides the zone system is only used for plant selection, not garden management. I helped set up another lawn forum and insisted that we make the member's location a mandatory field for registration. Now it shows up in every post. That makes it so much easier to help out.

Kimmsr--I guess I meant "feeding" and not "fertilizing". I understand the difference, but was unsure of what a good organic feeding schedule might be. I think Dchall answered that question though. However, how does covering the seam edges with a good soil mix rectify the situation? What do I do about any bermudagrass coming up through those cracks? Anything I can do about that or am I just going to have to live with it?

Dchall
So as far as feeding goes, would you recommend I do a feeding now as the sod is new or should I just wait until end of summer? Any info or maybe a link on amount per sq ft that is recommended for each of those products?

Also, as far as watering goes, I was thinking to continue at 1x a day for 2-3 weeks, then move to every other day for a couple weeks, and then space out the time a bit more and start letting it dry out before I water again. Am I getting this right?

Let your grass tell you when it needs feeding just as you should let it tell you when it needs watering. If it is growing good and healthy there is no reason to put down some nutirients like those that use synthetics which get washed out of the soil fairly quickly. As Dave indicated extra feedings probably will not do any harm to your grass although it may harm your wallet.
Putting some soil on the seams will help them stay moist which will help the grass grow back in. The open seams allow too much air which is harmful to the grass.
As I understand about Bermuda grass nothing will stop it.