One way to implement UBI, if we come down to it: a negative income tax for incomes below a threshold. It's relatively simple.
Independently of that, and regarding cost, the larger tax hike should be on the side of the employers. Here in Spain, employers pay taxes on behalf of each worker they have. Obviously that tax could increase a lot, because employers would be spending much less on wages. It also does not need to increase much the complexity of the system. AS a first order approximation (which is obviously naive), just apply a flat % increase to all taxes. In any case, when computing the real cost you should not count $800 per person, because many people, most people even, would not be getting richer with UBI.
Regarding 2), some proponents of UBI actually say that UBI is better than current systems regardin the disincentivation of work. Many countries do not have systems like food stamps and actually give monetary subsidies. It can often happen that if you work (or work more, or get a better job) you go over a threshold in income and lose your subsidies. In any system that's has at least some thought put into it, you will not get poorer due to that BUT it can happen that you see a ridiculous increase in your spending money. Then, why work? In a UBI system, wages would explicitly what you get 'beyond' welfare, everyone would know that, and these situations should disappear.
PS: When considering cost, also consider that UBI partially replaces other areas that may not be explicitly welfare: unemployment benefits, pensions, etc.