Ned finding out about Roberts bastards, and the seed is strong, is (imo) a hint to the readers about the Stark seed not being as strong

Arya looks like Jon. Arya looks like Lyanna. Ergo, Jon looks like Lyanna. That's what we're supposed to realize.

The "seed is strong" thing is a completely separate issue. It has nothing to do with Starks. There isn't a single piece of evidence otherwise. Magical Baratheon sperm provides evidence that Joffrey, Myrcella, and Tommen aren't Robert's kids. We need this evidence to exist so that Ned can discover the truth of their parentage. That's all.

How many Targs have black hair, dark eyes?

Rhaegar's daughter probably did. Why not his son?

we are told that he hasn't thought about the Rhaegar in years

Even if Jon is Ned's son, it's still pretty strange that Ned manages to think of Rhaegar so rarely. If it wasn't for Rhaegar, Ned's beloved sister, older brother, and father would be alive. He wouldn't be the lord of Winterfell. Catelyn wouldn't be his wife. He wouldn't have brought Jon back from the war with him, because the war wouldn't have happened in the first place. Ned's life would have been staggeringly different if it wasn't for Rhaegar.

Ned apparently manages to visit his Lyanna's crypt without thinking of Rhaegar. He must have one hell of a mental block. You really think Jon could break it?

Who leads him to think about Rhaegar? Dany. Who does he gets super defensive about? Dany.

Or, more precisely, Robert's desire to kill children (i.e. Dany and her unborn baby). Assuming Ned hid Jon's identity to protect him from Robert, this makes perfect sense.

Caitlyn asks Ned about Ashara and ned responds: "dont ask me about Jon" well she didn't... did she?

Yes, she did. She was assuming Ashara was Jon's mother.

that a couple months into this period she falls pregnant (you'd think there might be some problem here since her brother and father were just murdered by her new lovers father)

Robb's grief at learning that Rickon and Bran had been murdered led to his being "comforted" by Jeyne Westerling, a girl whose family served the lord whose grandson had killed Robb's father not long before.

Grief will, in many cases, cause people to be more likely to have sex. Not only that, you're also working off the assumption that Lyanna would blame Rhaegar for the stupid shit his psycho dad did. And that's assuming she was even told about it in the first place, and that she wasn't being held against her will and raped.

So 9 months later Ned arrives, grabs the new born child and runs off down to Dorne all to just bring Arthur Dayne's sword back to his sister, a girl Ned was infatuated with at the tourny of Harrenhall, and a girl his brother had been interacting with there.

While there he gives the sword to the Dayne family, he tells Ashara of her brothers death, and she supposedly kills herself out of a combination of this and that her recent child is supposedly a still born.

Ned then supposedly leaves with baby Jon up to winterfell.

How does Jon's parentage affect this?

If Dany is the child of Rhaegar and Lyanna, this means, what, that Ned showed up at Starfall and was like, "Soooo I killed your bro. Sorry about that. FYI here's the baby daughter or Rhaegar and my sister. Could you ship her across the Narrow Sea or something so Bobby B doesn't kill her? K bye." And where the hell did Jon come from, if that's the case? The oh-so-honorable Ned really did father a bastard somewhere? And he takes the baby from the mom because... why, exactly?

Lemons do not grow in Bravos

Apparently this may have started out as an editing mistake.

I would argue that it's not unreasonable to think that a wealthy Braavosi would dump resources into keep a single lemon tree alive, but that's speculation, so whatever. My problem with the lemon tree even being brought up in this context is that it gives weight to a R+L=D using little more than a plot hole. To say that this plot hole outweighs the evidence for R+L=J is... well, a tad silly.

I almost prefer the R+L=D+J people in this case.

Our only source on this really is her brother, hardly a reliable source and would have been too young to remember the truth. Instead we have Dany having memories that could not possibly be of Dragonstone or Bravos.

So Dany's memories of the lemon tree, which were formed when she was 5 or younger, are perfectly legit, but Viserys' memories, formed when he was 8, are unreliable.

Again and again she is told by Quaithe that she must remember who she is.

Which has absolutely nothing to do with whether Rhaegar was her brother or her dad.

If dany was indeed the sister of Rhaegar and born in dragonstone, how did she get to Dorne?

Probably the same way she got to Braavos: by boat. Also, this is what we call "special pleading."

Yet didn't he kill Arthur Dayne and drive his sister to suicide?

So... is Arthur alive? Ned lied about it in his own memories? Is Ashara alive too? I noticed your use of scare-quotes earlier.

And what the hell does that even have to do with Jon's parentage?