How can I create and keep these faces together nicely? My two questions are here, the rest of the text is a lot more context. Photo related to the context posted below.


How to create a square face in a larger face of which does not consist of perpendicular lines?
How to extrude out while keeping the sides flush with surrounding diagonal faces?


I'm in the process of making a small boat. The inside faces of it slope slightly inwards to the boat from top to bottom to create a "bowl," as well as the sides slightly splay outwards from back to front. I'm trying to create a bench in it that extrudes out from the back towards the middle of the boat that reaches from one side of the boat to the other, where someone would work the rudder. I'm also trying to create one in the middle of the boat for the oarman, so the only connections from that bench to the boat are from the sides, with space below. I'm very very new to Blender so I apologize if this is a very easy solution, but I can't for the life of me figure out a way to do that that isn't super janky.

CONTEXT FOR QUESTION 1. This issue is in the faces of the inside of the boat, being able to neatly create a face inside it to extrude. The faces are of irregular shape sow ith the default "inset faces" option, I can't find a way to make the face I will extrude be perfectly rectangular. I can do it by eye but I would definitely rather not if there's another, smoother way. My workaround solution has been subdividing the faces to get my desired height of the bench, but then it leads to my second problem.

CONTEXT FOR QUESTION 2. My second issue is when I can extrude, keeping everything flush with the splaying sides. This really only pertains with the bench in the back of the boat. When I can get a face I like that I can extrude, when I pull out towards the middle of the boat, the sides of it continue straight while the sides of the boat splay outwards. I cannot find a way to keep the sides of the boat and the sides of the bench together besides stretching it to fit by eye after I extrude. Is there a way to "snap" them together before extruding so when I pull it, it stays connected with the sides of the boat? 

I apologize if these are very easy fixes, I just for the life of me can not find a clear fix anywhere else online. 

Here's the boat in question, just for basic reference. That middle bench would be about where the x axis line is in the image, and the back bench coming out along the y axis towards you.
My previous answer won't give a correct method.

Actually the Snap option would work correctly if it was compatible with GG (slide vertex along an edge) but it's not the case yet.

What you should do to get edges perpendicular to the X, Y and Z axis is use the knife tool: K to activate, C to cut orthogonally to an axis, Z to cut through.



Once you've created an edge, you can cut again to create a parallel one, or simply select it and bevel with CtrlB.



Then again use the knife tool for vertical edges:



And when you begin to extrude, constraint on the axis you want: E to extrude then X to move the extrusion on the X axis.