I plant a peanut, lettuce, mustard greens, and spinach. After 3 weeks I noticed that my peanut have symptoms like yellow and brown dots on leaves. Several days later, the other vegetables get the same symptoms. But is it possible that the infection came from the peanut plant? Do fungi infect specific species or they can infect others?
Aaspergillus is a common mold that wouldn't have caused the issues your plants are experiencing. According to this site (look down the page for the various peanut diseases), your peanuts probably have either early or late leaf spot (Cercospora). These two diseases are nearly identical in look and effects on the plants. The good news is that they're specific to peanuts, so they won't infect your other crops. The bad news is that they can remain in the soil nearly indefinitely (see the linked site for some ideas on controlling these fungi).
As to your other question - "Do fungi infect specific species or they can infect others?" The answer is complicated. Some fungi can infect different species within the same botanical family. For example, members of the Solanaceae (this family includes eggplants, peppers, potatoes, and tomatoes) are notorious for becoming infected with the same diseases. Anthracnose can infect eggplants, peppers, and tomatoes, while Late Blight can infect all members of the Family.
In contrast, a disease called Gummy Stem Blight can infect some members of the Cucurbitaceae Family (this family includes cucumbers, squash, and melons), but won't infect members of the Solanaceae. And in contrast to the other fungi mentioned, fusarium wilt can infect all members of the Solanaceae AND it can infect members of the Cucurbitaceae, although the species of fungus that cause the disease may be different.
As you can see, there's no one Yes/No answer to your question. This is why it is always recommended that people who grow either or both Solanaceae or Cucurbitaceae rotate their crops on a two- or three-year schedule.
Now, for some really good news! In your own situation, you already are growing plants from four different Families:
- Mustard = Brassicaceae
- Lettuce = Asteraceae
- Peanut = Fabaceae
- Spinach = Amaranthaceae
This is already preventing your garden from being completely over-run with fungal diseases, as it is very unlikely that one fungus (other than downy mildew, perhaps) will be able to infect two or more of the plants in your garden. To prevent future problems with fungal disease, I strongly recommend that you not plant the same crop in the same location more than once every three years.