Abundant Step: "...a monk can slip magically between spaces, as if using the spell dimension door, once per day. Her caster level for this effect is one-half her monk level (rounded down). "
"...a monk can slip magically between spaces" A monk. Not a monk plus any companions.
But
"...as if using the spell dimension door..."
Dimension Door allows you to take others with you, within limits.
Empty Body: "...a monk gains the ability to assume an ethereal state for 1 round per monk level per day, as though using the spell etherealness..."
Again there is a reference to "a monk" and to "as if" using the spell which, on seem to contradict each other.
I think the intent is that these abilities are personal only and the spell tells you how it works - for anything not in the monk description itself.
However, given the way it is written, I could see a generous interpretation allowing the monk to use the spell targeting information.
The way I would play it is:
"...can the monk only bring himself and his normal gear?"
Yes.
"Does being heavily loaded interfere with these abilities?"
No. The restriction is limited to "When wearing armor, using a shield, or carrying a medium or heavy load, a monk loses her AC bonus, as well as her fast movement and flurry of blows abilities."