How long does a mosquito take to land on a host, bite, and fly off?
That's an interesting question and not easy to answer. I haven't found data for humans but from experiments with mice. They analysed how the mosquito actually bites, probes for the blood vessels (not all bites are successful) and finally sucks bloods. In their research  they observed feeding times between 150 and 329 seconds, depending on the size of the blood vessel. The mean feeding time was 240 seconds. It also depends on the age of the mosquito, older mosquitos suck longer. To this comes the time for probing (mean time 142 seconds) and the time before the mosquito starts probing after it landed (mean time 6.5 seconds). This totals to about 389 seconds (or roughly 6.5 minutes) total time after landing. This data can be found in table 1 of reference 2.

This is pretty interesting, they also show videos of the mosquito probing the skin for a blood vessel. You can find a pretty nice summary in the first reference and the original paper in the second:


Here’s What Happens Inside You When a Mosquito Bites
Visualizing Non Infectious and Infectious Anopheles gambiae Blood
Feedings in Naive and Saliva-Immunized Mice.