Before I post the pictures, let me summarize the questions we have:
(Q1) If existing framing is incorrect, are we really obligated to bring it up to code? Inspectors coming over to inspect rough in wiring will certainly see the existing framing that's exposed.
(Q2) So far, we've been DIY'ing, but we are not familiar with building code and house framing. To correct framing issues, are we better off hire a carpenter to tackle it, or do you think we can do it ourselves under the guidance from the online community like you guys? We've invested heavily in tools.

Now, could you please scroll through following pictures and provide inputs on how we could address each individual situation? Each image is linked to its full size image. I will number the paragraphs/questions.

First, the overview of the house. The wall we opened us is between the living room and the kitchen. We took the drywall down on the living room side.

The reason we opened up the living room side of the wall is there are some cracks from the corner of right opening that had grown in the last 5 years we lived here. Having the wall open will help us investigate.

Now, pics of the wall from left to right (standing in the living room):

(Q3) These two spans (sealed off by wood boards) are recent additions in 1994 done by the previous owner. That addition was permitted, so I assume the approach is up to code. The board on the right has crack in it. Do we need to replace it?

(Q4) The center part of the wall. It appears that the framing to the left is than to the right side. Actually the sheetrock on the left side was screwed on, and on the right was nailed on. Anyway, at the very top between beams, it doesn't really support anything because the roof/ceiling planks run lengthwise. So, is it okay that there are no studs up there in the opening at the top? The span on the right side has one 2x10 (actually 1.5"x9"), which appears to provide lateral stability to a roof joist on the back side. Is that up to code?

(Q5) The framing above the opening where we saw the cracks. Many things look wrong even to my layman's eye. At the left side, there is no cripple stud. There is no cripple stud to support where two horizontal plates meet, and the sagging there is visible. Is the correction as simple as throwing in two extra cripple studs?

The right hand side of the wall that we opened.

(Q6) The details at the top. As you can see, the big beam is not supported by a plate. It is indeed sitting on a wall. But it still appears to me that the beam was cut short and it should have its end supported. Does this need to be corrected?

(Q7) When we look closely at the big beams, it puzzles us how poorly they are connected to the rest of the structure. And some of them fractured due to the partial/broken shim underneath. How do we correct this?

(Q8) Now, about the sagging beam supports. This whole wall sits on a few piers that are supported by concrete blocks. In the crawl space, it appears that a couple of wooden piers have lost contact with the concrete blocks, thus not providing the support. The soil here moves quite a bit (we are in a hilly area), so most likely, the concrete blocks sank over the years. We plan to jack up the pier, rebuild the concrete foundation, and firmly support the wooden pier. Is that the right thing to do?

Sorry for the long post. Thanks for reading and we really appreciate your input, any input. We always learn so much from the online community.

To begin with, you're mixing up some of the terms, which makes for confusion. But you obviously have a lot more common sense than the previous owners and "handymen"!

I'm not trying to figure out the whole thing. But I will just comment on a few obvious things:

* the header over the opening (the fifth pic up from the bottom). It's absolutely inadequately supported. It should have been long enough to be supported on either side by a built-up post (several 2x4s or 2x6s nailed together--and there are even Code provisions for the pattern of that nailing. And even this assumes there is a bearing beam in the basement/crawlspace beneath.

*Yes, those shims are inadequate and don't even provide full support. Maybe they figured a lot of caulking/glue would hold it altogether.

*Those random 2x4s laid flat don't provide any useful support.

*The third photo from the top reveals five-six studs removed and replaced with one misinstalled diagonal 2x4. You ask, "Is this support up to Code?"
Uh, no.

To come up with the appropriate fixes requires an inspection of the structure of the house, additions and all.

"Up to Code." What a horrifying idea! Your helpful neighbours are taking the wrong approach. What you can't see can hurt you--especially if your house experiences a sudden structural failure. (Not to mention whatever electrical/plumbing "improvements" the previous owners made.)

If the municipality provides a free inspection, I would take advantage of it and follow their advice.

At the least, find a competent framing carpenter or a design professional who can design the corrections.

Actually, the 2x10 I was referring to are those pieces between the ceiling beams (e.g. in Pic #5 under Q5). The ceiling beams are much bigger. I think they are about 5(W)x12(H) (in cross section). But I think I get what you are saying -- that beam is sitting on a whole wall, so it's safe even though its end is not supported. That is indeed good news. :-)