I have a three-story house. Can I use a Mikrotik hAP ax lite as an access point to have one unit on each floor (I have thick ceilings) and if I create one wifi network will it work to switch between units when I go from level 2 to 0 for example?
I’m sure you could using capsman. I use 2 hap ac2 (old capsman - different configuration) but it works like a charm.
Preferably use wires to interconnect. Indeed this is a basic use case for CAPsMAN:
https://help.mikrotik.com/docs/spaces/ROS/pages/224559120/WiFi#WiFi-WiFiCAPsMAN
https://www.youtube.com/watch?v=bHotZT41w3E&t=89s
So there will be no problem switching between devices when changing floors if a capsman is used?
I have a 4011 router (that’s why I want to stay with Mikrotik products) and on each floor I want to connect the hAP ax lite as ap and to it by cable us or computer.
Which kind of internet connection (speed/bandwidth) do you have?
And which kind of devices (clients) do you have?
The RB4011 is a quite powerful/fast device while
the Ax lite is 2.4Ghz only, so not a very fast wireless access point, it has to be checked if they can represent ( now or in the near future) a bottleneck.
I have 1gb symmetrical fiber optic cable.
For now, I have all my computers connected by cable to the router.
Wifi is a minor addition for me. I need it for three laptops, three phones and up to five devices (if I ever decide to connect to the Internet).
I know the hAP ax lite ace is only 2.4Ghz, but on the above devices the most transfer it will probably eat up is Teams on video chat.
It is important to me that in hAP ax lite I can connect 1gb cable. Because my configuration will look as follows:
fiber → 4011 → wall outlet → hAP ax lite as ap → pc connected by cable on two levels and on one nas.
Just as a FYI, when the client wifi radio permits it, that AX Lite can push up to 400Mbps over wifi.
Teams does not eat much bandwidth, and 300-400 Mbps are anyway a lot, it is good to find someone that uses cables when needed and can live happily with a good enough wifi, in these times of wifi 6 and 7 crazyness. 
Just as a FYI, when the client wifi radio permits it, that AX Lite can push up to 400Mbps over wifi.
Surely I can limit the transfer
Teams does not eat much bandwidth, and 300-400 Mbps are anyway a lot, it is good to find someone that uses cables when needed and can live happily with a good enough wifi, in these times of wifi 6 and 7 crazyness. >
As I wrote, Teams is the application that will take the most transfer, so my wifi requirements are really low 
So in conclusion, the device I choose will work as I wrote? (once I configure it, of course) And there should be no problem switching between floors/devices when I go from floor 0 to floor 2, for example? (I want to make sure I understand this correctly).
WiFi AP switching is described here: https://www.youtube.com/watch?v=vkWPlsuyuKE