Helm of Mordicus provides +5 Fellowship when dealing with other Space Marines'

What exactly does that mean?

Some things are obvious ofc, other less so.

Like, would a Command test to order space marines around qualify?

Or a Command test to activate Tactical Expertise?

Or a Command/Fellowship test to resist Cohesion damage?

Like, would a Command test to order space marines around qualify?

Or a Command test to activate Tactical Expertise?

Or a Command/Fellowship test to resist Cohesion damage?

1. I would say yes.

2. This is the tricky one for me. I want to say no, but the fluff of Tactical Expertise is basically like telling your squad how your Chapter's pattern works and directing them to follow your orders on what to do to execute it, so probably yes.

3. I would say no.

"One does not simply 'Order space marines around'." Brother Bormir of the Ring Lords chapter.

Generally the helm applies a +5 fellowship to any fellowship based test involving space marines. Only when it is being worn though. In the event the same test applies to Space Marines and Non-space marines you may have 2 different reactions since the +5 might make a failure for non-marines a success (or greater success) for space marines.

As for ordering marines around...

The Kill-team is not the same as a normal marine squad in a chapter. While the leader provides direction, there is no requirement for the other marines in your team to kow-tow to your every whim. This is even more pronounced with space marines not in your kill-team. Whether members of another kill-team or marine chapters you aren't going to have authority over them unless it was specifically granted by those who have actual authority over them (meaning chapter captains, Deathwatch commanders... deffinately not inquisitors or Imperial generals, unless the space marines voluntarily choose to submit at their suggestion). The best you can hope for is to respectfully request, or leverage influence in these situations (which also benefit from the helm).