Okay, I don't really have a good answer for the first point of contention in chapter 7. The second one, yes, but here, I'm admittedly stumped, so of course I'm going to write far more than I need to in order to express my being at a loss for explanation.
So when the ark comes back to Israel, instead of taking it back to Shiloh (which would have actually made sense) they take it to Kirjathjearim, and put it in the house of a man named Abinadab. Here in 1Samuel 7, we are told it stays there for twenty years. However, the SAB rightly points out that when we compare dates, it's pretty clear that from this time until the time that David comes to carry it off to Jerusalem in 2Samuel 6, over forty years have passed, so what's up with that? I can think of a few possible explanations, but not many of them are highly convincing, even to myself.
One possibility is that by "twenty years", the author really means at least twenty years. It's possible, but not really too likely, since, if you're trying to express "that the time was long", forty years sounds better, and it's not like the author/editor of the book of Samuel wasn't aware of the true time span involved, since he wrote the latter passage as well. Note however that since we can say that the author did know the full story, something else probably was meant.
Another possibility is that this story is not in strict chronological order. While a possibility (since there are some stories in the book of Samuel that are clearly out of sequence), it's not likely. We are presented with the pretty clear picture that Saul was king for forty years, and if this happened during Saul's reign, it seems strange that Saul should not be involved in the story in some way.
Or are we sure Saul was King for forty years? Maybe it's just an error not here, but in Acts 13. It could be suggested, but that's not a really satisfactory resolution, both because we are still left with an error anyway (of some sort), and because I'm thinking Acts isn't the only book that says Saul was king forty years, although I'm not 100% certain.
The most likely explanation, although admittedly still not a very good one, is that the time span of twenty years is the span between the return of the ark and the events outlined in verse three and following. Thus twenty years would not be the total time that the ark was there, but the time between bringing the ark there and bringing the hearts of the people back to God, as apparently the people were very disheartened after their defeat and loss of the ark. Once they do turn back, Samuel calls them together and offers a sacrifice. (Edit to add: I note that the Ark was at least temporarily moved during the fighting in chapter 14. Perhaps that was 20 years later?)
This is the second matter noted by the SAB in this chapter, but a much easier one to comment upon. Who may offer sacrifices to God? Is it only Levites? Well, first of all, I have already argued that Samuel is a Levite, so that's not necessarily a problem. However, I'm not sure I'm convinced that only Levites may offer sacrifices anyway. There are certainly examples of others offering sacrifices, although admittedly most if not all of these are before the Mosaic Law.
Perhaps more important is the location, which is also noted upon here. There does seem to be a sentiment that at least proper, official sacrifices should be at the Tabernacle, and Samuel is not there in this story. However, consider that this is a special occasion with odd circumstances, the sort of which Israelites have had to wrestle with throughout history. The tabernacle is in Shiloh, but the ark, which is the centerpiece of the Tabernacle, is in Kirjathjearim. Given the situation, it may not have been very clear what was the right place for a sacrifice. Seeing as things turned out for the best, I assume that Samuel, who tended to hear directly from God on such matters, was told that this was sufficient for the situation.
Immediately following this, there is a battle between the Israelites and the Philistines, and the Israelites finally start winning, assumedly because God is on their side. I notice the SAB does not mark this passage with the usual markings that battle scenes get, but no matter; I'd just have to give my stock answer anyway.