How much time should I account to spend on the Keukenhof?

The garden is huge and I spent more than 3 hours inside because I wanted to see everything. You can skip the ticket queue by buying your ticket online. The problem with a day trip is only the drive to the place. It took me longer than it should have been because of the heavy traffic once I was almost there. But a day trip is still doable, especially if you don't plan to see the flower parade on the same day. As with your plan to make some stops in the Netherlands, I wouldn't recommend it unless you just want to see the cities at night.

It's not that bad, coming around midday and spending a few hours is perfectly doable. There will be some waiting at the entrance and a lot of walking but you can see a lot in, say, 3 hours. To give you a baseline, I have been to both type of attractions several times and often waited much longer at Amsterdam's main museums. Buying the tickets online can also make thing easier and save some time.

If you really want to see everything, you could also probably spend the full day there, coming early to avoid the bulk of the traffic around the area. The park itself also includes a few restaurants and is obviously keen on having people spend more money there but I typically don't stay that long and still manage to see quite a lot. Usually, my guests are quite exhausted by all the driving and walking and I don't plan any other visit for the day.

What you shouldn't expect is being able to drive there, park close to the entrance, get a ticket in a couple of min and be in and out in one hour. You wouldn't see much and spend a lot of money for nothing.

One day seems reasonable, but if you get bored easily, you can spend only half a day. It is very beautiful in Keukenhof, and not too crowded to enjoy the view. No, the line was not too long when we visited.

One day seems a bit of a stretch though, depending on what time you want to get there. 3/4 is more like it, but it depends on a person.

Living close to the Keukenhof I would suggest you come early in the morning, spend as much time in the garden as you like, and then check all of the flower fields around the Keukenhof. A full day should be enough even on busy days.

The "fast lane" is for people with prepaid tickets, so if you buy a ticket before you get there you're set. Of course a lot of people do just that so the fast lane at peak times may not be that fast :)

Very early is usually good. Be there just around the time they open if you can. From other tourist attractions in the area (I've not myself visited Keukenhof), busiest times for arrival are typically between 10am and 2 in the afternoon.
They open at 8 in the morning, so best you be there between 8 and 9. You'll have an hour or two before things get crowded to enjoy the place in relative quiet.
Tickets can be purchased online, saves finding a ticket bureau (and paying their surcharges): http://keukenhof.nl/en/plan-your-visit/tickets/ (but you will need a printer of course to print the tickets).