I have to say I'm not a pro in this field and I need help for solving this problem.
I have two internet connection connected to Ether1 and Ether2 ports of my Hap lite TC Router.
I have 2 questions:
1) Can I specify which device that connected to wlan use Ether1 or Ether2 as internet connection? For example my cellphone use Ether1 and my laptop use Ether2.
2) Can I specify a host name for using Ether1 and Ether2? I mean when a device that connected to wlan wants to access a website like mikrotik.com router choose Ether1 for internet connection and for the rest of websites use Ether2.
Thanks in advance

A well defined set of user requirements without any discussion of the configuration is best.

In your first statement WLAN has nothing to do with cellular.
Yes you can direct easily subnets and vlans out specific Internets
More work if you want to pre-ordain specific users.
Not easy to do on the fly for user - a quick and dirty way is to have available SSIDs per internet and thus person can choose that way, wired not so much.

1) Can I specify which device that connected to wlan use Ether1 or Ether2 as internet connection? For example my cellphone use Ether1 and my laptop use Ether2.

Yes. You can use dedicated SSIDs as @anav suggests, or you can use the hotspot functionality of Mikrotik or the WPA2-enterprise authentication (with username and password) on the same SSID to assign individual profiles to different devices, or you can use static DHCP leases to map a MAC address of the client to an IP address or to an address-list. But most contemporary phones use random MAC addresses to avoid tracking, so you would have to switch that off for your SSID.

2) Can I specify a host name for using Ether1 and Ether2? I mean when a device that connected to wlan wants to access a website like mikrotik.com router choose Ether1 for internet connection and for the rest of websites use Ether2.

This is only possible in RouterOS 7 where you can use regular expressions to add the IP addresses from a DNS response to an address-list, but it's not as easy as it may seem, because multiple domains may be hosted on the same IP addresses (like google.com and youtube.com, but less obvious combinations exist as well), so you cannot send google via ether1 and youtube via ether2 this way. Plus the devices must use the Mikrotik as its DNS resolver in order that this worked.