Could a widow like Lady Hornwood plead to their liege lord to not remarry? If they were being forced to marry could they seek help from their liege lord?

They could, and the lord might agree, because that might set up a scenario down the line where they make use of their right of escheat.

Or the lord might decide that they want to give that land to someone, and try to make the widow marry someone, or just turf out the widow altogther.

Depends on what the law was on widow’s rights, the deceased’s will, and so on. 

Did Renly know about the Stannis/Jon incest investigation/plans? Why didnt Renly bring Stark in on things, since he probably knew and had weeks of time being in the capital with Eddard but does basically nothing till Robert is dead. Or heck why not bring Jon Arryn in on the replace lannisters with tyrells plan?

Renly knew.

Actually, Renly did sort of bring Eddard in on it, rather inadvertently:

Ned was not sure what to make of Renly, with all his friendly ways and easy smiles. A few days past, he had taken Ned aside to show him an exquisite rose gold locklet. Inside was a miniature painted in the vivid Myrish style, of a lovely young girl with doe’s eyes and a cascade of soft brown hair. Renly had seemed anxious to know if the girl reminded him of anyone, and when Ned had no answer but a shrug, he had seemed disappointed. The maid was Loras Tyrell’s sister Margaery, he’d confessed, but there were those who said she looked like Lyanna. “No,” Ned had told him, bemused. Could it be that Lord Renly, who looked so like a young Robert, had conceived a passion for a girl he fancied to be a young Lyanna? That struck him as more than passing queer.

See, here’s the thing about Renly and the investigation: it is not in Renly’s interest for the truth to come out unless and until he’s succeeded in getting Margaery into Robert’s bed. Because if the truth comes out and Robert is unattached, then Stannis becomes the heir to the Iron Throne

However, if Robert is remarrying to Margaery, then the Tyrells replace the Lannisters in the King’s Landing power structure but because Renly’s brokered the deal and is romantically attached to Loras, they become allies to his faction. And while Stannis might temporarily be the heir to the Iron Throne, the moment that Margaery becomes pregnant, Stannis is out of the picture and Renly’s path to a Handship/Regency is clear. 

So what’s happening above is that Renly is both trying to get info as to whether the Margaery as Lyanna 2.0 thing will work but also seeing if he and Ned are sympatico, and neither works. It previews Renly’s pitch to Ned, in that he completely misunderstands how to appeal to Ned and win him over.

As to why not Jon Arryn, well A. Jon Arryn suddenly dying kind of makes that impossible, and B. there’s no reason to assume that Jon Arryn would favor Margaery – he might push for some other marriage. 

followup to the execeuting jaime question. i was refering to after eddard was executed by joffery. it seems weird to me that other than karstark, no one seems to even have suggested looping of jaimes head as retaliation. which seems pretty weird given that they were “a man has a right to vengeance” northmen, and most seems to have liked eddard a lot. you’dd think the suggestion would at least have been brought up

Ah, I see what you mean. Keep in mind, Ned was still alive when Jaime was captured, so the natural thought would be prisoner exchange. It’s not until the Battle of the Camps that they learn about Ned’s death, and yeah, it might have come up except for Robb being suddenly acclaimed King and now you need Jaime to get that peace deal. 

how can the dothraki bows shoot farther than the westerosi bows? youdd think that the people Who pride themselves on their capacity to wage war, and has immense number of wood to work with would produce better bows than the horse nomads of the dothraki sea, which is one huge ass open plain. great for horse gracing. not so much for finding timber.

Recurve vs. not, I would guess. Recurve bows also use horn much more than wood, fyi. 

why can an archer on foot outshoot one on a horse?

A couple things: first, because the horse is physically in the same space as the archer, in most cases this limits the size of the bow in question (hence why most horse archers used some sort of recurve bow to gain more power from a shorter bow) so you can’t shoot as far as a bow that’s as tall as the person wielding it.

But second and more importantly, an archer on the ground only has to focus on one thing: shooting as fast and as accurately as they can. A horse archer has to focus on riding the horse and shooting, which makes it more difficult to concentrate. 

Third, shooting while in motion is inherently more difficult than on the ground, because both you and your target are now in motion which means you have to make constant adjustments to your aim, and it’s further complicated by the fact that the gait of a horse means you’re dealing with both horizontal and vertical movement. 

What do you think Rhaegar hoped to accomplish by annulling his marriage to Elia? Do you think this will happen in the books or is Rhaegar annulling his first marriage a show only plot point?

Well, I imagine he wanted a legitimate child to be the third head of the dragon, but I’m of the opinion that Rhaegar reached back to Targaryen polygamy because it fits his whole scheme of trying to recreate Aegon the Conqueror as a solution to the prophecy of the Prince Who Was Promised. 

The fact that that scheme wouldn’t make much sense isn’t actually an argument against it, because in OTL him running off with Lyanna was the catalyst for war, so it never made much sense.