Ok. Based on your suggestion I found the solution for the question:

For the connection LAN client to the Internet I found my mistake. I forgot to add “modem” to the firewall zone wan.
The zone should look (at least) like that:

config zone
	option name 'wan'
	list network 'modem'
	option input 'REJECT'
	option output 'ACCEPT'
	option forward 'REJECT'
	option masq '1'
	option mtu_fix '1'

Of course, if we want to have also Ethernet cable wan connected, there should be those networks included:

	list network 'wan'
	list network 'wan6'
	list network 'modem'

If you, @alzhao have any comment for those solution, please do.

The still open question is:

I checked one more aspect. After ifdown modem, modem disconnects from the Internet. But next ifup modem does not connect modem to the Internet.