Do modern locomotives have air conditioning and/or lavatory facilities for the driver?

The newer locomotives have air conditioning, the older ones do not. Toilets yes, but they are not very clean...I'm being nice here...

The answer to both is "sometimes" and "yes".

As for air conditioning, generally only roads that cross desert climates will add airconditioning. It is not standard equipment.

As for lavatories, there is a toilet in the nose of the locomotive.

I am taking the term "modern" in your question quite literally, because only the most modern units come with lavatories standard. They used to be ordered optional, and some roads (such as the Norfolk Southern) thought they were saving money by not adding them. Their reasoning was that the runs were too short to make toilets necessary. This also negated any need to have the chemicals serviced, thus saving even more costs to management. Labor Unions have been the voice of reason, and conditions have improved.

There were also locomotives, such as switch engines and branchline engines that never strayed far from home and therefore didn't need a toilet, but such specialized engines aren't ordered anymore as railroads prefer using a standardized model throughout the road.

London Underground train have no toilets - however, there are toilets located at some stations that are accessable to the driver and staff only. Some stations have public toilets, but these are normally closed due to vandalism. Most modern and refurbished trains have cab air conditioning which occassionally works! We usually drive with the off side cab doors open during summer months.

Most modern locomotives that have been built since 1990's come equipped with Air Conditioning. Many older locomotives do not. As far as toilets, it depends on the railroad. Most Class I (Major) railroads have toilet equipped locomotives, many short line railroads do not have toilets on the units. There is no federal requirement for Air Conditioning or Toilets, but there are regulations concerning alternate toilet facilities for railroads that do not provide toilets on their locomotives.