Can I use tomato paste in dal? My current method for making an Indian dal include using whole peeled tomatoes, almost always canned. Would substituting Tomato Paste, the thick stuff from cans, change the taste, and if so, how? I don't mind the change in texture
Tomato paste is far more concentrated, and it's produced by actually cooking down the tomatoes a couple times. Since tomatoes contain a lot of sugar, this will actually caramelize those somewhat and produce a richer, sweeter flavor.  Even canned tomatoes will taste more acidic and less sweet.

So your finished dish will likely follow suit - it'll be a bit sweeter, have a slightly richer flavor, and it will have a bit less moisture.  That's not necessarily a bad thing; you may find that those different flavors interact with the spices in an interesting way.  Just make sure that you don't use a 1-to-1 substitution; because tomato paste is much thicker you'll want to use less of it or its flavor will totally dominate.