Vedic chronology is a mess. I don't think you'll find any satisfactory answers here because there is too much uncertainty in the field.

Traditionally, the Rig Veda is dated to about 1800-1500 BCE, based primarily on textual/linguistic analysis. But it clearly talks about events that are much older. It's hard to resolve this discrepancy.

The early Rig Vedic text describes its towns and cities as spread along the floodplain of the Saraswati. There has been a lot of speculation about what the Saraswati was, ranging from the Helmand in Afghanistan to Ghaggar-Hakra in India. It was mostly based on linking current geography to descriptions in the Rig Veda, but nothing really fitted. Now we're beginning to understand why - the river is not just dry, parts of it are buried under meters of sand in the Thar desert.

In recent years satellite imaging has shown a huge fluvial floodplain under the Thar, with alluvial deposits 5-30 meters deep, and up to 90 meters in spots. It roughly corresponds to the middle reaches of the Ghaggar-Hakkar existing today, the rest of it has disappeared. But there are still aquifers below the paleochannels you can see on satellite imaging, containing water that ranges from 40,000 to 4,000 years old. Low levels of tritium show that it's not rainwater that's percolated down there, it's the remains of an old river.

Meanwhile, climatology studies like this one show an abrupt weakening of the monsoon at ~2100 BCE. Also, the Aravali orogeny is still pretty active (and has been throughout the Holocene), so there is a frequent slipping of faults which periodically causes upheaval and subsidence of land in this region, and as a result rivers change course quite dramatically.

So the Rig Vedic text describes its own culture as spread along the Saraswati, but recent studies in climatology, thermoluminiscence dating of the Thar sands overlying the paleochannels, studies on spores and pollen recovered from paleolakes all converge on a date of about 2100 BCE for the most recent abrupt drying of this region. This implies that the Rig Veda is talking about events that predated this, which would put it solidly in Indus Valley territory, but how do you reconcile that with its traditional 1800-1500 BCE date?

The stuff you mention about nakshatras is interesting, but again it's hard to make sense of it. I don't know where you get the date of 2400 BCE for that, I'd be curious to know. Obviously there is no textual evidence going back that far, so I am guessing that you are using some kind of astronomical reckoning. But that is tricky and hard to get right.

The problem is that the Rig Veda isn't written as an astronomical text, it cares about ritual and it doesn't care to explain itself, it assumes the reader already knows these things. So it'll mention a couple nakshatra and you don't know if it's stars it's referring to or asterisms or asterisms in the sense of lunar mansions, as you say. If you want a clear unambiguous reference as lunar mansions in the Vedas, you have to go to the Atharva Veda, but then you are past the Rig Vedic period.

But you don't actually have to go to the Vedas for that, because the six Vedangas have also been copied and transmitted along with the Vedas. In particular, the commentary on Vedic astronomy by Lagadha goes into much more detail, and Lagadha clearly describes nakshatra as lunar mansions. In fact, the current system of 27 nakshatra was invented by Lagadha; before him there used to be 28 or 29. Traditionally, Lagadha's jyotishi is dated to 1400-1200 BCE by textual/linguistic means, but in fact the text itself contains its own date. He mentions that in his time, winter solstice is at the start of sravishta and summer solstice is in the middle of aslesha. Depending on how good his eyesight was and how much he approximated, that would put him somewhere in the period 1800-1500 BCE. I don't see why he should be very inaccurate. Unlike the Greeks, who used the solar ecliptic (which is hard to determine because you can't see the sun at night, so you can't be very precise about its position in reference to the stars), the Indians used Jupiter's ecliptic which you can see at night, and which is off the solar ecliptic by a small and known amount (about 1.3 degrees).

Interestingly, Lagadha mentions historical observations made by astronomers long before his time. You can calculate dates as far back as the late 4th millenium BCE from them. It's hard to know what to make of this. If you take it at face value, it means that these people had been staring at the stars and recording what they saw 5,000 years ago or more.

Anyway, there are a whole bunch of inconsistencies like that in the Vedas - they talk about a much earlier time and yet they appear to be composed around 1800-1500 BCE.

As for your question about being contemporaneous with Indus Valley, it's very likely they were, for a time. The Rig Veda (even the latest parts) mention nothing about the disappearance of the Saraswati, nor the abrupt climate change. Those are huge things. It seems very unlikely that they wouldn't make into the text somewhere. It's not until the Brahmanas or the Mahabharata that we find mention that the Saraswati is gone and now there's a desert there. Why don't the Vedas mention Indus Valley? Well, I don't think Indus Valley thought of themselves as "Indus Valley". From the perspective of the Vedic writers, perhaps there was nothing to write about. They were well-integrated with the local populace at the time, so there wasn't any "us versus them" to write about. Vedic Sanskrit has a hell of a lot of loan words from Dravidian languages, so they were obviously written when the Indo-Europeans had already been in India for long enough to integrate all those words. It was yesterday's news.