Bold as Brass - Comparatives

This is a lovely short expression with a triple rhyme in it:
'Snug' = comfortable and cosy (e.g. two parts of a machine might 'fit snugly together'; many pubs have a 'snug bar' where there is a fire burning in winter and people can relax and be comfortable together)
'Bug' = a small insect, such as a fly or beetle
'Rug' = a (probably fairly small) piece of carpet, perhaps along the floor in a hallway; or if you are going off by car for a picnic, you might bring one with you to spread out on the ground before you sit down.
'As snug as a bug in a rug' suggests that the little insect has made itself comfortable at home in the soft surroundings of the rug.

A snail must be one of the slowest-moving creatures in all of nature; but so would most of us be, if we 'had to carry our own house along on our back'!
You may have noticed that many of these 'as ... / as ...' expressions work particularly well if there is an echo between the sounds in the two ideas: either they alliterate (e.g. they each start with a B, as in the quiz title), or perhaps they rhyme. If the sounds match, that makes the comparison seem stronger, doesn't it? In this case we have 'slow ... snail', and the letter S in English quite quickly suggests a lot of other slimy, slippery, slithery unpleasant things like snakes and slugs and maybe also spiders. Some other languages have this feature too: how about yours?

There are plenty of other expressions for this common idea: 'as quick as lightning' (since nothing else travels as fast as light), or 'as quick as quick could be'.

Nothing on earth seems to be more dazzlingly white than snow, so this is what we use for this comparison (although, like many of them, it probably isn't quite literally true!).

Gold is traditionally among the most precious things in the world (if we ignore diamonds, and before they discovered platinum) ... so what could be better than a 'gold standard'? (And helpfully, Good and Gold both start with G; we can almost hear the baby chuckling gently to itself, smiling and charming everybody else!)

You might hear almost any of these, and plenty of others.
1. A chocolate teapot would (fairly obviously) melt, and lose its shape, and generally be 'unfit for purpose' if you tried to put a hot liquid inside it.
2. Instead of a barbecue, with lots of fairly small pieces of meat, some people prefer the old tradition of slowly cooking a whole pig ('hog') over an open fire. For those who like such things, no doubt that's fine ... but there are plenty of people who don't, such as vegetarians, Muslims and Jews. Bar-mitzvah is a Jewish celebration (the 'rite of passage' when a boy officially becomes a young man), so a gathering of Jews would be unlikely to want a hog-roast, because they regard pigs as 'un-clean'.
3. Quite a good phrase, but we don't seem to use it.
4. If you have spent any time in Britain you will know how depressing a rainy day can feel in the middle of a long working week. Nobody wants one of those! But this is not the usual situation to use such an expression. You might just as likely use it to describe someone who arrives looking angry, who will not join you in polite conversation.

This one DOESN'T rhyme or alliterate ... but what could ever be warmer, or more comforting, than a fresh slice of toast?

A cucumber has a delicate flavour and it is succulent, with a lot of refreshing juice in it (almost like a 'naked cactus', without the sharp needles on the outside!).
Anyway, in English we can describe someone's calm behaviour as being 'as cool as a cucumber', meaning that they do not become at all 'hot and bothered', even in circumstances where they might grow angry or embarrassed.
Incidentally, we would have said 'an ice cube' rather than 'a cube of ice' (Answer 3).

Beetroot is the dark red root-vegetable that is sometimes put into salads, and (famously) into Russian 'borshch' soup. There can't be many other common, natural things that are such a deep red colour. If you have ever had to wash up after a meal that involved beetroot, you will know how the colour spreads and lasts (and it also turns blue if you leave it to dry). Of course, a human face should never turn quite as red as that ... it's just an expression!

'Light as air' is also possible, but probably less usual; there is also an expression 'free as air'.