Good questions – all three points are feedback effects that would likely have some impact in the direction you suggest. I will explain my reasoning for thinking these would be small.

(1)
Currently tax evasion accounts for a £5.3bn per annum[1] gap – this encompasses income tax evasion, but also includes VAT evasion, capital gains evasion, etc. Even if we assume that all of this is income tax evasion, and assume that the change in incentive doubles the amount of evasion, an additional £5.3bn makes up about 0.8% of income tax receipts. Using these fairly extreme assumptions, we end up with a <1% impact, so in the hopefully more likely scenario that only ~50% of the 5.3bn is income tax, and UBI increases evasion by only ~50%, we end up with a 0.2% impact which is (I would consider) fairly negligible. Then you have the fact that (at least in the UK) most middle class people pay their taxes through PAYE, which is administered by the company they work for, so there is less opportunity for them to benefit from "under the table" payments.

(2)
Someone has done some good analysis[2] of some UBI-esque schemes in North America, and has concluded that of the people included in the experiment, an average of around 10% left the workforce. The person doing the analysis views this as an unacceptably large number, but these schemes were only targetted at low-income groups, so there is a large selection effect. People on higher incomes are less likely to accept a large reduction in the their standard of living. Even if we make a generous assumption that 30% of the working population are sufficiently low-income that this 10% statistic applies to them, we have a reduction in the workforce of 3%.

As a very, very rough calculation of the economic impact of this (using the US, as the studies were in North America), there are 155m jobs in the US, so losing 3% of the workforce translates to 4.65m jobs. As these are low-income jobs, let's say they pay on average $20,000 p.a. - that results in a productivity reduction of $93bn. The US GDP is $20.5tn, so that would correspond to a 0.45% reduction to GDP - as a one off hit, I would consider this negligible. In the UK, I would expect this to be even smaller, as our existing benefits system is more comprehensive and generous to start with, so we are starting from a different position.

(3)
The first thing that makes me fairly confident that this would be a small effect is the fact that immigrants on average contribute significantly more in taxes than they consume in government services. It takes effort and motivation to uproot your life, and often a job offer is required in order to get a visa anyway. In order to receive a UBI, the government has to know that you exist, so undocumented immigration wouldn't be encouraged. Factors such as job availability, general state of the economy, language and existing immigrant community play significant parts in where and whether people immigrate, but it cannot be denied that generosity of state support may be a factor in some potential immigrants' decision making.

It is a complicated issue with many facets, but thankfully someone at LSE has already done some regression on the effect of welfare on immigration[3]. This analysis uses a "de-commodification factor", that "refers to the degree to which individuals, or families, can uphold a socially acceptable standard of living independently of market participation". In the Western countries it analyses, this factor varies from 18.3 in the US to 35.9 in Norway. Their regression analyses asylum seekers separately from economic migrants, and shows that a 1 unit increase in this factor increases asylum seekers by 11.9% (with R squared of 0.63), but actually decreases economic migrants by 2.06% (with R squared of 0.52). Given that only about 35,000 of the 627,000 immigrants to the UK in 2018 were asylum seekers, I think this suggests a fairly small impact.

On the emigration of net payers, I would simply say that the proposal above doesn't actually affect high earners much at all - the effective tax rate of anyone earning £120,000 or more has gone up by 1.8% or less. The most that anyone's effective tax rate goes up is 5% (for people earning between £46k and £100k). Some people would probably be spurred to seek their fortunes elsewhere by this, but 5% is well within the bounds of a normal governmental policy shift, especially if spread over several years. There don't appear to be any particularly good studies on this, but the most mobile people are the ones that are the most rich, which is why this proposal doesn't include a higher rate bracket targeting them.

[1] https://www.patrickcannon.net/insights/uk-tax-evasion-statistics/
[2] https://www.chrisstucchio.com/blog/2019/basic_income_reduces_employment.html
[3] http://www.lse.ac.uk/government/Assets/Documents/pdf/research-groups/msu/WP-2012-02.pdf