I am not a petrus expert by any means but:
// By the way, this is basically an expansion on what @Thom S. said, and it took me about 10 mins to write during which there is a new post so I am replying to your first question
EO (edge can be hard to understand at first, but gets better with some practice (e.g learning how to do ZZ). There are some rules to determine if an edge is oriented:
For edges with U/D stickers:
Edge in top/bottom
If the U/D sticker faces the top or bottom, the edge is oriented
Edge in middle layer
If the U/D sticker faces the front or back, the edge is oriented
For edges without U/D stickers:
For these edges, look at the F/B coloured sticker.
Edge in top/bottom
If the F/B sticker faces the top or bottom, the edge is oriented
Edge in middle layer
If the F/B sticker faces the front or back, the edge is oriented
An edge that is oriented can be solved with only the moveset <R, U, L, D, F2, B2, M2, E2, S2>. In the case of Petrus, after building the 2x2x3 block, orienting the remaining edges leaves the rest of F2L to be solved with only R and U moves.
How to orient edges
The easy way
-Put the block on the left
-If there are no oriented edges, do F' U* F (* means any type of this move e.g. U/U'/U2). This only happens rarely but it's good to
check
-Using R/U moves, put an oriented edge at DR
-Now follow these steps for any misoriented edge:
1) Use R* U* R*' to put it in the middle layer on the front
2) Use F' U* F to orient the edge, replacing another misoriented edge from the top layer.
3) Rinse and repeat
The harder but better but still intuitive way
-Certain triggers like F' U* F flip 2 edges at a time
-Other triggers like S R/R' S' or S U/U' S' flip 4 edges at a time
-You can use R/U moves to set up to either a 2 or 4 flip (in the case of a 6 flip, just learn an alg for it or make it into a 2 or 4 flip with a trigger), then do the 2/4 flip alg.
Hope this helps
// Wait actually, I guess I can answer your second question now:
Yes, OLL will only be with corners. This type of OLL is called an OCLL by the way.
There is a subset of 1LLL (1 look last layer) called ZBLL (we are considering a name change due to reasons stated in
this thread )that is 1LLL with EO done. It has 493 algs, so only those at a very high level will learn them, but it is a thing.
COLL can also be used to do OCLL while solving the corners, giving an edges only PLL.