Can i store a UInt32, Int32 and a float value inside a double without losing information?

Being able to store the maximum value of UInt32 without losing information doesn't necessarily mean you'll be able to store all values in UInt32 without losing information - after all, there are plenty of long values which can be stored in a double even though some smaller values can't. (2⁶² can easily be stored exactly in a double, but 2⁶² - 1 can't, for example.)

However, you are okay - the mantissa for double is 52-bits long, so any integer with fewer than 52 bits can trivially be stored as value * 2⁰ (i.e. an effective scale of 0).

And yes, float values can be converted to double with no loss of precision too.

However, note that this doesn't mean that 0.1f == 0.1d for example - it just means that (double) 0.1f is exactly the same number as 0.1f, in a different representation.

It's also worth noting that Int32 doesn't have a smaller range than UInt32 - they both have a range of exactly 2³² consecutive values. However, Int32 does have a smaller "absolute" value, and with the way that sign is represented in floating point values, that's relevant. You still actually need 32 bits in order to store the absolute value of every Int32, because Int32.MinValue is -10000...0000 in binary (32 bits in total), or -(2³¹ + 1).

Finally, float isn't just double with less precision - it's got a smaller range too. It only has 8 bits for the exponent compared with 11 in double. So there are numbers well within the range of double which are outside the range of float, even if they don't have many significant (binary) digits.