Is it possible the algae/fungus is moss? If that is the case the problem might be compacted soil and improper pH. Proper lawn pH will help with the weeds as well. If you have evergreens that drop their leaves, you'll have a higher pH in that area as well.

Sounds like you need to add some lime. Check your local extension office for instructions on how to send a soil sample. They will give you a report that will include the soil pH and other info depending on the level of test you order.

If it's moss you should be able to just scrape it up and throw it away. I have a similar problem in part of my lawn that doesn't get a lot of sun, the soil is too acidic and compacted. Some of the moss grew back this year so I'm going to aerate and add lime.

You'll probably want to aerate your soil as well around mid August. A core aerator is better than a spike aerator when it comes to loosening compacted soils.

Aerating your soil will also help the roots grow deeper. This should help your grass become more drought tolerant. You can rent a core aerator or if you have a small area the Turf Hound from Hound dog seems pretty good. It's also good for areas where you can't get the big gas powered aerator to go. I just ordered one of these and am waiting for it to arrive.

When you do seed that bare spot, cover it with straw, mulch or dried grass clippings to help keep it shaded and moist until it germinates.

Since you're dealing with drought frequently, you may want to also consider seeding with a good tall fescue seed. They do better in these conditions. After aerating the soil would be a good time to overseed your lawn.

Personally, I don't like the look and feel of tall fescues, especially when mixed with other grasses. It stands out like a sore thumb. But if you're having a hard time growing other grasses this might be the best thing to do. From what it sounds like on your property, after a few seasons of overseeding with tall fescue, it will probably become the dominant grass in your lawn.

If you can get a good turf going and mow high and leave the clippings on the lawn you should be able to keep the weeds down. You might also want to cut back on the synthetic fertilizers and weed control in arid climates. From what I've read, organic lawn care programs tend to need less water than synthetic.

I've been looking into organic programs for the past year or so and will start using one this season. This is the organic lawn care program it looks like I'm going to start. I haven't found local suppliers for the items and I like that they mail me what I need when I need it. I haven't been keeping a good schedule for lawn care so I hope that helps me.

good idea to do a soil test before getting too far into this.