should I rack my home brew to 3rd Carboy or bottle it?

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You can rack again if you plan on lagering. But as far as yeast in the bottom of the bottle, that is unavoidable. You need some yeast to make it into the bottle so that your priming sugar will be eaten during bottle conditioning. If your friend doesn’t like yeast in the bottom of his bottle, tell him to buy you a filter and a kegging setup so you can force carb.

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Tell your friend to grow a pair…..

If the fermentation is completed, I wouldn’t personally want to expose my beer to the possible contamination. Assuming you are bottle conditioning, than some yeast sediment is unavoidable. Remind your friend that bottle conditioning and the resulting sediment is beneficial to your beer and any sediment you accidentally consume is very healthy – it’s vitamin B!

A gentle rest in the fridge while cooling and a smooth, careful pour into your favorite drinking vessel (you wouldn’t drink fine wine direct from the bottle would you? don’t do it with beer either) leaving the last half inch in the bottle will leave almost all of the yeast behind.