Hello, I'll try to go point-by-point to answer all your questions.

Please keep in mind that these are my personal opinions and should not be taken as facts.
What criteria do clients have before they decide to pay for art?
When I commission an artist, I look for: quality, style, price, skillset. These are my personal preferences, and this will vary with different clients.
- Quality is how good their art is, which I can see from the examples they provide. A newer artist might not have a lot of quality to their work just yet. This factors mostly with experience.
- Style is how the artist draws differently from others. A cartoonist will draw characters differently than an anime-focused artist. I try to find which style I'm looking for.
- Price is how much the artist is charging for their work. This has many factors, such as the quality and style might increase the price, which is totally fair and reasonable. My budget for commissions helps determine how much I'm willing to spend.
- Skillset is how many things can this artist do, such as character design and background art. This isn't a key factor and more of a nice-to-have. If an artist is good at characters but not backgrounds, I probably will only commission them for characters. However, if an artist does more I will likely commission them again for different types of work.
How do artists decide their price list?
This really depends on other factors that morinoir mentioned. The way I tend to estimate price is based on hours of work. (Note some artists charge a base price instead of per-hour rates.)
For example, where I live in the USA the minimum wage is about $8 an hour. This is the MINIMUM though, and art is considered part of entertainment which is priced and valued much higher than this. So let's say you would charge about $20 an hour, which is just an example. If a piece of work takes about 10 hours, then the base price would be $200. There are many other factors that can go into this, such as the client requesting changes to the design, complex character design or background, etc.
What helps determine price is your skill level and how much time you put into a piece of work.
- Your skill level could be determined by how long you've been drawing, if you went to school for art, and generally the quality of your work. It's not reliant on these factors, however, since some people are naturally talented or self-taught and this does not devalue the price of their work. It's hard to determine since this is more of a personal evaluation.
- The time mentioned includes concepting, sketching, linework, coloring, backgrounds, etc. Remember that your time is valuable and a client should respect that (and pay you accordingly for it).
Opinion about my art; how much do you think it's worth?
I'm very impressed by the wonderful art you have here! I really admire the clean lines and detail in your characters, and the attention you've put into the backgrounds really makes each piece stand out. You have very good art!
For what your art is worth, this is hard to say. Personally I would pay $20 per hour easily for work of this quality, which may actually be underpriced. However, I do not know how long it takes to make each artwork, so I could not tell you what the total price would be.
A really helpful thing you could do is to look for other artists that share your style and quality of work and see what they are pricing for their artwork. This could help you determine what to price your work at.
Please keep in mind that this is my personal opinion, and I would suggest getting more opinions before deciding how to price your work.