'By Friday 1st May' means on or before this date. 1st May is the deadline. This means that it's fine to do it before this date, or - at the latest - you can do it actually on this date. For example, if you have to complete an application and hand it in, it will be accepted at any time before the office closes on the evening of the 1st May. In effect, it means 'before 2nd May'.

It means "before" in this sentence.

The word "by" has many meanings. It is a preposition, so it is used to form more cohesive sentences. By can mean, 1. around 2. over the surface of 3. a mode of ( ie. by candlelight or by car) 4. past (ie. he walked past the dog) 5. during (ie. by day) 6. at or before (by noon on the third day) So confusing, I know. Just try to use context clues