RADICES | Rank Degree Influencer Core Sampler

First of all, for normative information on PDF you should refer to the appropriate ISO standards, in particular ISO 32000. Yes, Part 1 (ISO 32000-1) in particular is derived from the PDF reference 1.7 without that many changes, but not without changes either. (Ok, in some situations one has to consult the old PDF reference, too, to understand some of these changes.)

Adobe has published a copy thereof (with "ISO" in the page headers removed) on its web site: https://www.adobe.com/content/dam/acom/en/devnet/pdf/pdfs/PDF32000_2008.pdf

Now to your question:

According to ISO 32000, both part 1 and 2:

An integer shall be written as one or more decimal digits optionally preceded by a sign. [...]

A real value shall be written as one or more decimal digits with an optional sign and a leading, trailing, or embedded PERIOD (2Eh) (decimal point).

(section 7.3.3 "Numeric Objects")

Thus, concerning your question a)

is the notation correct (as provided in the examples?

Yes, 10000000000 is an integer valued numeric object, 0.00000000000000000000000000000000000000000000000001 is a real valued numeric object.

Concerning your question b)

does pdf format expect implementations to use (or at least fall back to some bigint/bigfloat handling) of numbers, as it seems to not provide any range for the numbers?

No, in the same section as quoted above you also find

The range and precision of numbers may be limited by the internal representations used in the computer on which the conforming reader is running; Annex C gives these limits for typical implementations.

and Annex C recommends at least the following limits:

integer 2,147,483,647 Largest integer value; equal to 2³¹ − 1.

integer -2,147,483,648 Smallest integer value; equal to −2³¹

real ±3.403 × 10³⁸ Largest and smallest real values (approximate).

real ±1.175 × 10^-38 Nonzero real values closest to 0 (approximate). Values closer than these are automatically converted to 0.

real 5 Number of significant decimal digits of precision in fractional part (approximate).

(ISO 32000-1)

Integers Integer values (such as object numbers) can often be expressed within 32 bits.

Real numbers Modern computers often represent and process real numbers using IEEE Standard for Floating-Point Arithmetic (IEEE 754) single or double precision.

(ISO 32000-2)

I know they all represent the same value but does Java mark their differences somewhere?

No. You did, when you wrote the source code, but the compiler converts them all into binary: no information as to the original radix of the numeric literal is retained.