in short, can I claim FSA dependent care for my preschool going toddler. I work but my wife does not. Does it matter in claiming it? I read irs page but I didn't understand. Can someone explain please.
If your wife has no earned income, and did not look for work in the period, then no, you may not use a Dependent Care FSA nor claim the childcare tax credit, unless your wife was mentally or physically unfit to work.
The rules are nearly identical to the Childcare Tax Credit, and that has a very detailed explanation in the document linked above, part of which I reproduce here:
Earned Income Test
To claim the credit, you (and your spouse if filing jointly) must have earned income during the year.
Work-Related Expense Test
Child and dependent care expenses must be work-related to qualify for the credit. Expenses are considered work-related only if both of the following are true. They allow you (and your spouse if filing jointly) to work or look for work. They are for a qualifying person's care.
There is also a diagram in Publication 503 (linked above) which details all of the tests you must pass to claim the credit (and, similarly, FSAs).
If your wife earned some income, you may be eligible for the credit, as long as it wasn't "nominal" income. However, if you're simply looking to write off your preschool costs which you'd have incurred anyway (regardless of your wife "working" or not), you're probably violating the spirit of the rule (particularly the Work-Related Expense Test).