If that's the case, you need to date more often.

Yes you can grow basil in your climate but it should be grown in part shade so it doesn't get the hot afternoon sun. It shouldn't have wilted in a few hours inside. I have grown it in my south facing window all winter, but not in your heat. I only say this to show you it can be grown inside. Did you check to see if it needed water. The next mistake you made is putting it outside in the sun. This plant was probably grown in a greenhouse and needed to be hardened off before going outside permanently. It had never been exposed to uv light and it has to be introduced gradually. Can you imagine what would happen to a person who had never been outside and was suddenly put outside in the sun--the same with plants. To harden a plant off you put it outside in the shade for a couple of hours and then bring it in. you gradually increase the time it is out and gradually increase the sun. In your case and location morning and late afternoon sun. Basil is very easy to grow from seed. It sprouts fast and is usable in a month, so get yourself some seeds. I imagine your weather has cooled a bit now so you might be able to plant it in the sun now,

Forget twice a week, water when the plant is dry. That might be every day. 50% shade cloth would help with the desert sun altho I don't know where to get a small piece, just the big rolls are at any greenhouse supply. Try total shade during the hottest hours, full sun morning and evening.

Growing tomato's here is a bit different than in other areas of the country due to the sun intensity and heat. Plant tomato's as early as possible but you must also watch over early "starts" due to the cold weather than can still arrive in Feb & sometimes early March. They need protection from evening temps. Star has tomato protection from cold weather. Tomato's will grow, should flower and produce fruit all Spring long especially if any of the many cherry or patio tomato's are grown, also medium size tomato's such as Celebrity or Early Girl are easier to bring to maturity. Beef Steaks, large tomato's are not nearly as easy. When the temps go above 90* the tomato's will no longer set blossoms, therefore not tomato's. If left in the intense summer sun, the plants will often dry up and die. Many people have better luck growing their vegetables under shade cloth here through the summer and get good results. Also tomato's can be planted in containers, once over 90*, cut the tomato's back by half, place them in the shade, continue to water and bring them out again at the end of Sept. into the sun. The plants will begin flowering and developing tomato's. You may have tomato's (though green) up to Nov or Dec. Watch for frost temps. and pick any tomato's left on the plants, place them in paper bags to ripen. If you feel that you are not getting good pollination, you can take a small stick and shake the plants a bit. You should be able to see pollen being released so that you can be assured your plants are getting the necessary pollination. Of course good fertilization every 6 weeks is advisable whether regular or organic. Growing tomato's here is a bit different than in other areas of the country due to the sun intensity and heat. Plant tomato's as early as possible but you must also watch over early "starts" due to the cold weather than can still arrive in Feb & sometimes early March. They need protection from evening temps. Star has tomato protection from cold weather. Tomato's will grow, should flower and produce fruit all Spring long especially if any of the many cherry or patio tomato's are grown, also medium size tomato's such as Celebrity or Early Girl are easier to bring to maturity. Beef Steaks, large tomato's are not nearly as easy. When the temps go above 90* the tomato's will no longer set blossoms, therefore not tomato's. If left in the intense summer sun, the plants will often dry up and die. Many people have better luck growing their vegetables under shade cloth here through the summer and get good results. Also tomato's can be planted in containers, once over 90*, cut the tomato's back by half, place them in the shade, continue to water and bring them out again at the end of Sept. into the sun. The plants will begin flowering and developing tomato's. You may have tomato's (though green) up to Nov or Dec. Watch for frost temps. and pick any tomato's left on the plants, place them in paper bags to ripen. If you feel that you are not getting good pollination, you can take a small stick and shake the plants a bit. You should be able to see pollen being released so that you can be assured your plants are getting the necessary pollination. Of course good fertilization every 6 weeks is advisable whether regular or organic.