If the GM allows it, your friend could now use the alternative to the Beast Master ranger which appears in Tasha's Cauldron of Everything (TCoE, p.61):

Primal Companion, 3rd-level Beast Master feature, which replaces the Ranger's Companion freature.

This option has more synergy with class development - possibly mult-classing, too.

This alternative to the ranger sub-class does not rely on CR; it says:

You magically summon a primal beast, which draws strength from your bone with nature. [...] When you finish a long rest, you can summon a different primal beast. The new beast appears in an onoccupied space within 5 feet of you.

The Primal Companion alternative also provides three options to choose from for your companion, a beast of the land, of the sea or of the sky. Your ranger's companion will also evolve as your PC increases in ranger levels, proficiency bonus modifier and spell attack modifier - hence the synergy.

• Ranger Levels increases: Hit Points
• PB increases: AC, damage
• Spell attack modifier increases: to Hit bonus (attack modifier)

Not only that, you also get a way of returning the beast back to life:

If the beast has died within the last hour, you can use your action to touch it and expend a spell slot of 1st level or higher. The beast returns to life after 1 minute with all its hit points restored.

If your friend wishes to multi-class with a Rogue, it might be worth considering the sub-class of Mastermind (XGtE) at level 3, as he'd be able to use Master of Tactics and use the Help option as a bonus action to give his Primal Companion (beast) an advantage on attack rolls. This would mean that the Ranger would need to use one of its Attack actions so that the companion attacks. Still, it's a fair synergy. I would not multi-class until the ranger reaches 5th level though, as the Ranger will need the Extra Attack to increase their damage output and versatility.

Officially, probably not...

There are no precise limits provided that state exactly under what circumstances an item is attended, except that the item be "grasped, touched, or worn" (PH 166), and attending an item is the usual bar for determining whether an effect that affects only a creature also affects that creature's gear. (Further, attending an item also allows the item to share the attender's saving throws.)

Thus, the DM must decide if the mount is attending the cart. While the mount is technically touching the cart, that seems a little suspect given the cart's size, and a DM that permits the mount to attend the cart must, for example, also rule if, by extension, a captain on deck attends that ship.

...But this is cool enough that this DM would allow it

It's really hard for a low-level PC to take a forge (or an alchemist's lab or a water clock) on the road, and I think most dwarf gods would approve of a dwarf paladin using his holy mount for such a purpose rather than—or in addition to—war. ("Crafting weapons is war!" sayeth the dwarves... or something.)

As long as nobody else could be considered attending the cart when the mount's dismissed, this seems a reasonable use of the special ability. However, I'd draw the line at allowing the mount to attend multiple carts.