I more like to use "ts/tv" for transition-to-transversion ratio. This abbreviation had been used in phylogenetics. When NGS came along, some important developers started to use "ti/tv", but I am still used to the old convention.
Why is the expected value for random substitutions for the Ti/Tv ratio 0.5?
There are six types of base changes. Two of them are transitions:
C<->T and the other four types are transversions. If everything were random, you would expect to see twice as many transversions – ts:tv=2:4=0.5.
If the ratio is expected to be 2.10 for WGS
The expected ratio is not "2.10 for WGS". It is 2–2.10 for human across the whole genome. You see this number when you align the human genome to chimpanzee or when you focus on an accurate subset of human variant calls. However, in other species, the expected ts/tv may be very different. Also, this number is correlated with GC content. You get a higher ts/tv in high-GC regions, or in coding regions which tend to have higher GC, too. Partly as a result, it is hard to say what is expected ts/tv in exact.
but I get 3.00 what does that mean? What if I get 1.00?
If you get 3.00, your callset is highly biased. If you get 1.00, your callset has a high error rate. Suppose the exact ts/tv is $\beta$ and you observe ts/tv $\beta'\le\beta$, you can work out the fraction of wrong calls to be (assuming random errors have ts/tv=0.5)
This is of course an approximate because $\beta$ is not accurate in the first place and because errors are often not random, so their ts/tv is not really 0.5.
How exactly does this ratio imply false positives? Too high ==> high false positive rates? Or too low?
Too low ==> high false positive rate; too high ==> bias. In practice, you rarely see "too high" ts/tv.