There have been a few attempts (mostly in EU novels) to discuss the properties of the blade, but most analysis instead explains why Jedi (and Sith) could use the blade effectively despite the objections you correctly raise.

Here are the things we know:

The weight of a lightsaber is comparatively light, and the mass is entirely in the handle. (We don't know the weight of the handles; they're thicker than a real sword hilt but hollow and filled with electronics. It's probably comparable to a heavy longsword hilt.)

The 'blade' is a magnetic 'bottle' containing the plasma generated by the lightsaber. It generates a strong electromagnetic field. This means that the blade will have a little resistance to motion when in the presence of ferrous metals (most of the time, in SW). The blade will, therefore, 'bounce' off some metallic substances, even as it melts them. (The duel in ESB has some good examples.) The dense magnetic bottles are certainly the reason the blades 'bind' on each other rather than passing through each other.

(Note that when Jedi burn through bulkheads and doors, they always insert the lightsaber at right-angles, point first. Clearly this is to avoid lateral resistance from the magnetic field.)

Apart from these magnetic effects, the blade is effectively weightless.

The basic handling, therefore, would be extremely hilt-heavy. The natural balance point is probably all the way back inside the user's grip.

As you correctly point out, this would make the blade extremely hard to 'feel'. This goes a long way to explain why only Jedi wield lightsabers. (This also explains the usefulness of the training remotes; they cure the tendency to overcorrect the blade. The first lesson Jedi are taught is to discard their physical senses and feel the blade position with the Force. Clearly this is not just a teaching style but a practical necessity.)

Jedi must develop extremely strong wrists. This is not a problem; like medieval knights, Jedi begin training at a very early age, including lightsaber training from day one. Clearly this is, in part, to build wrist and arm muscle. Note that Luke - who does not have this training - consistently uses his lightsaber two-handed at first. He doesn't (and clearly can't) use it one-handed until he's gained much more experience and practice.

The heavy two-handed styles in common use in the original trilogy are clearly, therefore, a matter of control. As with real longswords, the extra hand on the hilt provides control and direction, not power. (Lucas directed the actors in the original trilogy to behave as if the blades were extremely heavy... hence the kendo-like styles. This makes sense; an old man and a wounded cyborg would no longer have their youthful wrist strength and control, and would have to be cautious.)

These drawbacks conceal advantages in disguise. Sure, they're a problem in a swordfight. But Jedi aren't primarily duellists, they're police. Their 'typical opponent' is a room full of people with blasters. The blade-light overcorrection that harms 'feel' in the bind also gives you rapid tip movement to stop a flying blaster bolt - if you have a Force sense telling you where the tip should go.

(Note that Sith, who typically do expect other swordsmen as enemies, frequently seem to wipe the floor with Jedi in a straight swordfight. Compare Dooku's tight, defensive style - and note the curved hilt of his lightsaber, letting him keep the blade forward without pronation of the wrist. Likewise, Maul's staff-style avoids the whole 'feel' problem, at the cost of reach - and an intense danger of cutting off his own leg.)

This is why non-force users don't wield lightsabers - without the precise Force sense of blade location and combat movement, they're likely to overcorrect and hurt themselves. And without the intense training, they wouldn't have the strength and stamina to control it. (This is canon; note that in the EU, Talon Karrde considers the lightsaber at Luke's belt to be proof of his identity by itself. "You were either Luke Skywalker, Jedi, or else someone with a taste for antiques and an insufferably high opinion of his swordsmanship." Clearly, without Force training it's not possible to develop sufficient control to use the saber effectively.)