First, you have to convince yourself that, assuming this is the only MAJOR 'issue' w/the house, you REALLY want the house. If the answer is YES, then it's time for your Home Inspector to pay a visit.
Hire someone that's either an ASHI-Approved Home Inspector, or someone that's not ASHI-Approved but has the PROVEN qualifications. The $300-500 fee is money WELL spent to hear that the 'problem at hand' may cost you 1000's of $$$ later on. AND, his fee is a WHOLE lot cheaper being 'stuck' w/a BIG problem along with a mortgage that's costing you 10's or perhaps 100's of 1000's of dollars (over time.) In short, you can pay now or pay later.
It's hard for me to tell what this wall and trench are doing. From the sounds of it, the wall is 'trying' to keep water out and the trench is 'trying' to channel whatever water gets behind the wall, away from the house. I guess it doesn't sound like it's working from your description of the situation. Again, w/o seeing this, the calcium deposits may be efflorescence but maybe not. Effloresence is a 'power' that's given off by concrete when a lot of moisture is 'passing through' it. If the wall is leaning TOWARDS the house, I'd be concerned. This is an indication that the pressure on the far side of the wall is PUSHING it into the trench. In due time, you'd have to replace that.
Now, assuming the Inspector says you have a problem and it's going to cost $15000 to fix. (Yes, you can request an estimate for 'repairs' as part of the inspection. ASHI-Inspectors do this.) Then, you have to decide if you have that kind of $$$ to make the fix, AND you should take it into consideration when you BID the house. Assuming the home is selling for $115,000 and you're willing to settle for $100,000, then, deduct another $15,000 (to $85,000) and $85,000 is now YOUR top-out price (not $100,000.) Soooo, you'd probably start your bidding at $75,000 and END at $85,000. See what I mean?
For me, the EASIEST decision is to get the inspection. From there, you can decide. If you don't have the $$$ for Inspections, you should look at another home (where 'problems' are less obvious AND you're more likely to buy.) My best to ya and hope this helps.