Problem 1:

If Robin corp distributed dividend to Nancy,she will report the dividend income on her tax return. Thus the income that has already been taxed at the corporate level is also taxed at the shareholder level.If Robin distributes $100000 of dividend to Nancy and assuming Nancy has no other income sources,her taxable income will be $ 90,500 (100000-5800-3700).She pays tax at the preferential rate applicable to dividends received by individuals.Her tax is $ 13575.
Dividend distributions are not deductible by corporations, but corporate shareholders are entitled to dividend received deduction and shareholder can apply preferencial tax rate on constructive dividend.
Paying $ 100000 as a salary would get the corporation deduction in contrast if corp pays dividend it won’t get the deduction for the same.
If Nancy receives $ 100000 as salary she will have to pay tax of $ 35000,instead if she receive $ 100000 as dividend she will be taxed at preferential tax rate of 15 %. So it is beneficial for Nancy to receive dividend.
From Robin corporation point of view dividend distributions are not deductible so they will have to pay tax of $ 35000 . If Robin pays $ 100000 as salary, they are entitle for deduction.

Problem 2:

Section 351 provides that gain or loss is not recognized upon the transfer of property to a corporation solely in exchange for stock,however if taxpayer receives property other than stock (i.e. cash or boot) from corp,realized gain is recognized.
For transactions to qualify as non taxable under sec 351,the property transferor must be in control of the corp immediately after the exchange.Control means that the person or persons transferring property must have at least an 80% stock ownership in the corp.

Joe has ordinary income of $ 10000 on the transfer because services do not qualify as property.Joe has basis of $ 10000 in newco corp.