Do you endorse clay pot irrigation? It seems so useful for gardens and raised beds, but I don't see much information on it.
This is an ancient method thought to have originated in China.
Here is an article.
http://permaculturenews.org/2010/09/16/ollas-unglazed-clay-pots-for-garden-irrigation/
When should you water your vegetable garden? In the morning? Doesn't it just evaporate or in the evening? Does it cause mold? Thank you!
These articles should help: https://www.gardeningknowhow.com/edible/vegetables/vgen/water-plants-vegetable-garden.htm
https://www.gardeningknowhow.com/garden-how-to/watering/watering-garden.htm
On Gardener's World on 12th June, I heard Monty Don say that plants in outdoor pots may only need watering once or twice week. He said that they would perform better with a full watering occasionally rather than a drip watering system twice a day. Is this the case, as I have always used an automatic watering system twice each day.
Watering depends on some many things, type of plant, pot size, potting medium and soil, temperature, wind conditions.
You really have to check the soil and water as needed.
More water will be needed as temperatures rise.
Here is a great article.
https://www.gardeningknowhow.com/special/containers/container-plant-watering.htm
How much water is enough for a veggie and flower garden?
Typically, the garden needs about an inch or so of water each week. It is a good idead to water deeply (for about 20 min. or so) every other day or two, depending on the weather. Once temps reach 85 F and up, daily watering is often necessary. Those in containers will need twice a day watering.
If a plant is being watered by a sprinkler system and the foliage and a portion of the soil (but not all of the surrounding soil is getting wet), is the plant getting enough water if the sprinkler is running for twenty to thirty minutes?
It is typically not recommended to water foliage only because this can lead to fungal infections when the plants are not or unable to dry off due to poor air circulation. Therefore, bottom watering or drip irrigation is generally preferred. This does not mean you cannot use overhead watering, however. Simply do it at a time when you can ensure that the plants will have plenty of time to 'air out' so the foliage will dry.
For watering amounts, the rule of thumb is 2"per week. Normally with drip irrigation you can measure this by placing a small cup or jar in the area being watered and seeing how long it takes to fill it to 2 inches, usually 20-30 minutes. Overhead sprinklers would likely take much longer as the water is not going directly into the soil.
I have not had success with my vegetable garden for the past 2 years. I'm told it's because I'm watering with salt treated water softener and I must tap into the water line prior to the softener. The mystery is I use the same water for my flower and herb gardens and have no problem. Vegetables seem to not grow or produce. Also, we've had extreme heat and drought. What do you think?
I would start with a soil test.
You can contact your local county extension office for help with this.
This will help you determine if the salt is building up in the soil.
https://www.gardeningknowhow.com/plant-problems/environmental/softened-water-and-plants.htm
The use of a rain barrel is a good option for watering.
Here is a link for you.
https://www.gardeningknowhow.com/garden-how-to/watering/collecting-rainwater.htm
Should I water the hillside around 9 a.m. when the sun is coming up or around 7 p.m. when the sun is going down?
This article will help. Though it's aimed at vegetables, it really covers ALL plants and would apply to your situation as well: https://www.gardeningknowhow.com/edible/vegetables/vgen/water-plants-vegetable-garden.htm