Grammar Inversion

No. Anyway, the meaning is not at all clear.

You might rewrite it as "I am reading at home.", or "I am reading in the house" if that's what you mean.

Nor really. Your meaning seems unclear but...these are some suggestions:

I am reading at home.

I'm reading in my home.

If you're using the sentence in a poetic or artful way, say "Reading in the house is I." You'll sound Shakespearean.

Some people who are native speakers of English do use that sort of expression.

A fast car is me.
Rare roast beef is me.
Stylish clothes are me.

One might allege that it is ungrammatical, but there are people who will use that locution to mean that the thing or activity mentioned is very important to them. It's not something you would probably want to use in writing (unless it were dialogue), but using it in speech is acceptable.

It would work if you used it narratively. Drawing back the curtains and peering through the window, you'll see someone sat in a chair. That person, in case you ask, reading in the house, is me.

Or you could just say, I'm reading in the house.

When I first read it, Jane, I thought your meaning was along the lines of Toys 'R Us.

It's certainly grammatical and it's definitely acceptable within the narrow confines that have been described in this thread by Setanta.

But it is uncommon because it is an unusual word order.

Or "Reading in the house am I".