How to go from Poipet to Siem Reap: in the afternoon and especially IN THE NIGHT?

Do the pick up trucks still ply the route since buses started doing it?

I'm not sure. Maybe someone knows this better.

About afternoon train: I do not be fooled by the official online schedule. The train makes it into Aran around 19.00 or 19.15. I NEVER made it before that and the train left on time. I m not sure whether this is the result of the epic construction work along the line and might change some time in the future.

The Thai side had me through within 5 minutes as did the Cambodians. I would calculate not more than 30 min for both check points and the walk between both.

Keep in mind that you need to get to the border which is about 6 kms from the train station. You might be able to share a tuktuk with other passengers. I did this once at 20 bath and once I paid a motorbike 60 baht after haggling.

No buses at that time as far as I know - I am pretty sure there are non as their economics involve various scams that depend on certain arrival and departure times.
You best bet is to ignore anyone and do no speak to anyone, walk to the roundabout and negotiate with the camry drivers. Pay only at arrival at your hotel. They will try to drop you off elsewhere or at 'their' hotel and play any sort of stupid games.
I never had trouble around 8 or 9 PM in Poipet along the main road.

morning train: They have a converted truck in Aran which serves as a big tuktuk. Was about 20 bath years ago when I took it.
Border: Depends on the week day. Weekend is visa run rush hour. Unfortunately, many take this train, the BKK buses around the same time and it is a zoo. The visa is your least concern as it adds not too much. The long lines at both checkpoints are a headache. I always take the afternoon train. The bus makes it very sure that you arrive late in Siem Reap, they delay departure, arrival etc.
In short: the travel takes the entire day no matter when you leave.

Generally, in the evening the scammers are gone with few being left waiting for a gullible arrival. It is not a whole crowd descending on you.
As for taxi prices - I never took one. There is plenty info online. Unless you appear really desperate for a quick departure the late hour should work for you. Your trip is an additional job for the driver.There is no competition for that ride.
I hope this helps somewhat.

Forget the buses and their games, I'd look for a camry as Mike said. Taken them a few times, no more than 10 dollars.
Pick up truck are a thing of the past on this route now, the road is paved and it's not 1998 anymore.
Always have a place to stay in your head, even if it's not your exact choice but in the area you want, that way they will drop you where you want to be, not just some out of the way place on Hwy 6.

First case
The first thing I will do is taking an afternoon train to Aranyaprathet (arrived ~1800).
1. How long does it take for immigration process without having to apply visa at 7pm?
* Depends on the ammount of visitors there, however not having to apply a visa it should not take more than half an hour.
*Have you checked that you even need a stamp in your passport. Perhaps you do not.
2. When arriving in Poipet, is it safe to stroll around the main road at night (for finding bus companies)?
*Yes, especially if you look like a SE Asian.
3. Which bus providers provide the transportation to Siem Reap in the night? How much is it and what about the schedule?
*I doubt that there is any.
4. About the free governmental shutle bus, do they run until night; or can I still take the 12$ government taxi? And do they provide hotel drop-off?
*Government taxi? They might tell you they are . . .
*Forget the government bus. They take you out to a bus station where you are stranded and have to wait until they fill up the bus.
The last time I was on one, they dropped off 5K-6K from downtown so their pals could make money off taxi fares.

Second case
I take a morning train to Aranyaprathet (arrived ~1200).
1. How long does it take for immigration process without having to apply visa at 1pm?
*Maybe it will take longer because earlier there will be more visitors around. Maybe an hour.
2. Which bus providers provide the transportation to Siem Reap in the afternoon? How much is it and what about the schedule?
*I doubt there will be any, but you could try a 100 yards past the traffic island. They tend to leave in the morning.
3. In case I take the government monopoly bus, where will I be dropped in? And what time will the bus arrive?
*Refer above. 5K - 6K from downtown.
4. For taxi, how to find and take a shared taxi to Siem Reap, and how much does the trip cost as per 2016?
*Last time $10 sharing with two other Cambodians. The taxi picked up others on the way and dropped them off.
5. Apart from taxi and bus, I read from some sorces mentioning about pick-up truck services that go to Sisophon and Siem Reap. Do they have the schedule (rough schedule: first round and last round)? Where can I find them?
*Being Asian, there is a slim chance that you can flag as truck down and ride as a passenger for say $6, but it might be a slow trip.
About the touts, that will attach themselves to you like flies on **.
Tell them you are only over to shop or gamble on the border and have a hotel booked.
Walk a 100 yards past the traffic circle, and look for cars parked with drivers.
Don't take a motor bike to this area, they immediately become touts when they let you off.
Touts put up the prices because the taxis have to pay commision to them.
If you travel by shared taxi to Seam Reap, don't let them take you to any hotel. They receive commission and put your price up.
To go from Aranyaprathet to the border, I once stood by the side of the road waving B20, and a coach took me.
But if it is too hot, just offer a motor bike B40.
Do not go to the Cambodian border office on the Thai side. It is a fake.
I'm surprised some people still for for it but they do.
Happy travels.

Thanks for your information, but are there many tourists heading to Siem Reap in the night? And one more, are Camry drivers reliable?

Thank you very much for detailed reply! I'll consider about it.

You might travel to Siem Reap at night. I don't know I have never tried.
Are Camry drivers reliable? They always have been, but don't pay up front and don't let them put your bags in the trunk.

The trip to Siem Reap is not that long. The bus company does all it can to stretch it out. As for the camry drivers. They are usually pretty good - as far as my experience goes. They depend on a functioning car and avoid risks. Again, just my experience and there is no guarantee.

The problem with the Poipet - SR stretch is that there is no really good solution. During the day the scam industry is in overdrive and in the evening not many tourists. that's why you will fly through immigration and do not have to wait for hrs.

Please let us know how the trip went. Always good to have the latest update and readers will appreciate it.