DHCP and gateway

aren’t the leases all dynamic? (the D in DHCP)

Nope :)

Dynamic = could change because there is no reservation in the server (in practice the device tends to get the same address each time if the lease hasn’t expired on the server)

Static = the address has been made reserved in the server so that MAC (and only that MAC) is given the same IP each time.

Manually assigned – you did the work on the client and the DHCP server isn’t consulted.

Many people confuse static and manual. Many supposedly qualified IT techs¹ confuse the two so non-IT-techs shouldn’t worry too much.

The advantage of static from a reservation is that the machine can be given a reservation in various different networks on different sites (for example) and when plugged in at that site they will have a predetermined address automatically. DHCP – do the config once and then forget it exists, manually assigned – repeat the technical exercise every time you move the client from one network segment to another.
I spend all day with a network with many network segments (none are more than 254 IP’s per segment to keep the broadcast domain small) and the LAN portion is about 4,500 devices at any one time the wireless is only about 800. I really wouldn’t fancy trying to deal with that on a manual addressing scheme.

Don’t know but every other week (approx.) I have to turn off the ADSL router and turn it on again to renew things.

Look for newer firmware – it sounds like a memory leak

¹ GE medical seem to specialise in this field :-(