What's the maximum possible wealth bonus that a d20modern character can achieve by 10th level, excluding DM intervention? What is the max at 20th level? How rich would such a character be in real world dollars?
The conditions required to get the maximum possible wealth bonus are very artificial, but for the sake of argument let's assume the following:
Such a character can start with a wealth bonus of +20 at 1st level (8 from the 2d4 roll, +6 for Dilettante, and +3 x2 from taking Windfall twice).
At level-up, there are three ways the wealth bonus might increase:
So we can figure out what the maximum theoretical wealth increase is for each level by tracking the things that give bonuses to the Profession roll (Wisdom, Windfall feats, and ranks in Profession), and comparing that to the current wealth rating (which is the DC for Profession checks when leveling up). We can then calculate the maximum bonus from the Profession roll, from new Windfall feats, and from the flat bonus from having ranks in Profession. That's summarised in the following table.
As you can see, the wealth bonus quickly becomes so large that it becomes impossible to beat the DC on the Profession check even when rolling perfect 20s. (And note that 20 is not an automatic success, see p. 44 Skill Checks.) After 4th level, only the Windfall feats and the flat bonus matter.
To find the maximum wealth bonus at a level, find the wealth bonus in the table and add the total increase for that level.
So, the maximum wealth bonus at 10th level is +70 (wealth bonus starts at +64, plus the total increase of 6), and the maximum wealth bonus at 20th level is +135 (wealth bonus starts at +127, plus the total increase of +8).
As for how much that is in real-world dollars, according to the system there is no way to translate it into dollars:
So a character with +70 Wealth is rich enough that credit is easy enough to come by that they almost never need to worry about money. For comparison, the table on p. 38 calls +31 and higher "Very rich". The only purchase that could even be noticed by such a character (i.e., which would drop their wealth by any amount) would have to have a Purchase DC of 85, which means they could have as many mansions (Purchase DC 36), Learjets (Purchase DC 40), or M1A1 Abrams tanks (Purchase DC 47) as they wanted to own. The only way money would ever be an object would be if the GM set an exorbitant custom DC for, say, buying a very large rival company.
A character with +135 Wealth is so exceedingly rich that they don't ever have to even think about money—their wealth is so great that everyone knows they're good for it, and their vast network of accountants pays for everything out of the complex financial empire they own. They probably don't even know exactly how much they're worth, and considering how the stock markets work, their exact wealth is probably impossible to know until they tried to use every last penny of it, at which point there would probably be world-wide financial panic. They can probably buy entire countries, unofficially.
If you manage to roll an 8, add 6 for the Dilettante Profession, and 6 more for Windfall x2, you'll start with 20.
If you're allowing cybernetics and have PL9, you can buy windfall as a cybernetic feat implant at DC 26. If you succeed 4 times, your wealth would be 22, 24, 26, 29. Once you are above 28, you can buy a Feat Plex (PL8) at dc 28, and fill it with 3 windfalls and a cybertaker feat.
You can repeat this as many times as you would like and have infinite wealth and every feat in the game at first level.
@SevenSidedDie has covered the first part of the question thoroughly. As for conversion to real world dollars, there is a table on page 145 of d20 Future (ISBN:0786934239):
The relationship between purchase DC and item cost is roughly exponential:
Note that this is the price of an individual item that a character might purchase - not his or her total net worth.
For example, a character with +64 wealth bonus would lose 1 point when purchasing an item valued between $500 and $650,000,000; 2 points for items between $900 million and $12 billion; 1d6+1 points for items between $15 billion and $50 billion; and 2d6+1 points for items costing more than $50 billion (provided that they succeed on their wealth check).
Regarding large starships:
d20 Future Tech (ISBN:0786939494) has some example starships and mecha, including a PL6 light freighter with Purchase DC 56 (+5 if purchased in PL5) and an orbital colony with Purchase DC 72.
Given that the Space Shuttle Endeavour cost approximately $1.7 billion (Purchase DC 67), that seems a little low. The International Space Station, believed to be the most expensive object ever constructed, cost between 35 and 150 billion dollars (Purchase DC 78 to 83).