For me the indication would be the invitation. You say that your friend sent the invites but with your address. Do you mean that guests are RSVP'ing to you? If that is the case then yes, as a guest I would absolutely think you are throwing/hosting your own shower.
Nothing else that you mentioned is indicative of who is hosting the shower IMO.
Sorry - to clarify - friend sent the invite to the guests which said "Baby shower at [Rockstar's address] on xxx date, please RSVP to [friend @ phone number and email address]"
I *think* what we're doing is OK, but I guess I'm caught in the dilemma of helping out a friend who offered to do something nice for me, but is clearing struggling, and the perception of the guests that I'm a self serving, shower hosting gimme pig. I'm leaving all the decisions to her - games, decor, even food (ie: husband makes it, but she picks the menu) but I'm willing to help with labour. For example, she found some quiz/fill in the blank type games, but I made some photocopies of them for her.
I'm worrying about my husband's "chef pride" too - he'll make the food, but I don't want him to do anything to fancy that we couldn't pass off as my friend's cooking. Not that we'll lie, but I don't it to be obvious... although my husband does take great pride in his cooking so I feel like he'll want credit for it
As far as who is paying - she's going to cover decorations, games, favours, etc. but the grocery cost was never mentioned and frankly I feel too weird to ask, so I think DH and I will just pay for them, unless she offers.
Is it also alright that my mom said she's also going to help by lending us a punchbowl, coffee urn, etc. and providing a fruit tray, and one of my aunts RSVPed to my friend with an offer to provide baking? These are guests, so I don't think they should have to, but I also didn't want to turn down their generous offers so my friend asked if I was OK with that, I said sure, if they are sure they are up to it. Is that OK??