Scyph - my boat has many of the issues you're wrestling with at present so I felt compelled to reply to your post. From the photographs you've provided it appears to me that the prior owner has completely disconnected the bilge pump hoses. On My E-27, the electric bilge pump uses that smaller diameter white hose, and feeds in aft (toward the back of the boat) of the yellow manual bilge pump's black hose through a "T" fitting (similar to yours in the photo). It's tough to tell, but it appears that on your boat the manual bilge pump has been completely removed and that the hoses have been disconnected from the above-waterline thru-hull on the transom (that's the flat, vertical back of the boat). The white hose should lead from the thru-hull on the transom all the way to the electric bilge pump in the bilge area near the galley. On the port side transom on my boat, the slightly upper and outward most above-thru-hull is connected to my fuel tank vent, and the inside and slightly lower thru-hull is connected to the bilge pump hose.
I would strongly recommend that you wire a new circuit for the bilge pump. Don Casey's book has an excellent diagram and instruction in it for wiring a 3 way switch to be used with a floating switch for the bilge pump. I would not chance the proper functioning of this essential component on the prior owner's handiwork. I have had to do the same. I found the float switch dangling loose in the bilge with taped electrical connections under water. Not good.
As for your fuel tank, absolutely heed the advice that others have provided and get it out of the lazarette and stow it somewhere in the cockpit or perhaps somewhere on the "house", bungee corded to the handrail when not in use.
You have a decision to make as to whether or not you should plumb a new fixed inboard tank or to use an external tank with your outboard engine. Determining factors here will be more evident when you evaluate the size of your outboard, it's thirst, and your requirement for being under power in getting into and out of your slip in the marina, the how often you'll find yourself under power in your local cruising grounds under typical conditions. I myself would insist on an inboard tank properly secured, vented, and with a new bilge blower and plumbing installed. Aside from the tank itself, I am at present redoing all the bilge blower plumbing, wiring, and fitting a new inline bilge blower for my inboard Atomic 4. Total cost, even at West Marine, has been a less than $100 project to make her safe. The advantages to using the external fuel tank is that it can be vented to the open air, does not present a combustible safety hazard to the boat from leaking vapors into the bilge, and is easier to refill since you can take it with you. The disadvantages are that you need to find some way to secure it in the cockpit while underway so that it will not move around in a seaway, live with reduced range while under power, and contend with the fact that it takes up precious space in the cockpit.
Best of luck getting her cleaned up and orienting yourself with your new to you boat. tackle one system at a time in order of safety and you'll do fine. I love my E-27, basket case that she is at the moment while sitting on the hard. They are fine boats and the mechanical and electrical systems will become more obvious with familiarity and research as you undertake refitting them.
Skol!
-Ike