Spelling Bee - Homophones

There is no need for any apostrophes here: nothing has been shortened, no letters therefore lost, and there are no possessives in either the singular nor plural form.
'Whole' = all of something ('He ate a whole grapefruit'); 'hole' = a gap, as in 'a hole in the wall' or 'a hole in the knee of your trousers'.

You have to go right down to Answer 4 for all the details to be right on this one ~ rather like 'going down on all-fours' to clean the pine needles off the floor after you've packed away a Christmas tree in January!
In order: 'real' is not the same as 'reel' (which is a cylindrical container onto which you would wind-in a wire or thread, such as fishing-line, recording tape or film, or string, knitting-wool, thread etc.). In the days before television, people who went to the cinema would see a 'newsreel', i.e. one reel full of film that would show them the latest news as the film un-wound and passed through the projector. This word ('reel') also has further uses, e.g. a drunken person may be 'reeling about' (moving in an un-coordinated way), or someone with a lot of knowledge may 'reel off' a series of facts, such as the names and dates of all the Kings and Queens of England. (The image, here, is like of a whole 'string' or 'chain' of information coming off a reel.)
Christmas is an established religious festival, so starts with a capital letter, and (in honour of Christ of course) has a T in the middle ~ which tends not to be clearly pronounced when people wish one another a 'happy Chris-mas'.
Conifers are not supposed to drop their needles, as deciduous trees do with their leaves in autumn (see the earlier Question about Burnham Beeches!). But they may ~ just about ~ be said to 'leave their leaves'; 'leaves' in the latter sense, being the slightly irregular plural of 'leaf' (like 'knife / knives', 'shelf / shelves' etc.)

'Past' (as in 'past tense') is an adjective; 'passed' is the past form of the verb 'to pass'. These two forms sound pretty well identical, and such are often confused in writing even by native-speakers.
It may help slightly to remember that 'What has passed, is past' ( = 'Whatever unfortunate words or situation may have come between us in times gone by, that's all over now, so we can look more positively to the future').

Only one of these four sense-related words has an odd spelling in English. The related noun is 'signature' (from the French; but in English pronunciation you can hear the G sound more clearly). We talk of the 'signature tune' of a t.v. show (the piece of music that identifies the programme straight away, even if you aren't watching), for instance. But if you have travelled to Britain or are thinking to, we are sure you will know all about being asked to provide your signature on your identity documents.

Each of the offered alternative spellings for 'poor' does exist in English:
'Pour' = to tip some liquid out of a container, so that the liquid runs under control into another container ('Pour me a coup of tea'); we also talk of it 'pouring with rain'. 'Pore' = a small hole in one's skin ('He seemed to be sweating out of every pore'; it also has another further meaning); 'paw' = an animal's foot. They all sound more or less indistinguishable.
'Too' sounds like 'to' (the infinitive particle and preposition: 'I want to go to London') and 'two', the numeral (= 2 !). But only this spelling can be used as the intensifier (' ... too drunk to keep himself awake').
Be careful when making/using the past form of verbs such as 'drop => dropped', 'trap => trapped', 'log => logged' etc.: the single consonant on the end of the present form needs to be doubled in order to keep the sound of the vowel short (thus keeping the sense easier to recognise). Meanwhile, 'off' and 'of' (though each very common) are not the same word. In some parts of the country you may even hear, for instance, a parent say to an adventurous child, 'Get down off of there'!
... And finally: don't confuse 'one' ( = 1 !) with 'won', which sounds the same and shares two letters, but doesn't mean the same thing. In a knockout sports championship (e.g. Wimbledon), several players go in at the start, and everybody loses eventually ... apart from The One Who's Won! ~ the Champion, Andy Murray or whoever.

Only Answer 3 has all the correct versions. The sentence means 'Will they not wish to wash ... ?'
The false vowel in 'wash' (A pronounced as O) is perhaps the trickiest point in this example.

You should know 'know' apart from 'no' by now; 'it is' becomes 'it's' (with an apostrophe to mark the lost letter), and none of the other possible spellings/punctuations of this tiny word would be right here.
'Rain' is the water that drops frequently out of the sky; 'reign' (which sounds identical) = to be king or queen (as in the National Anthem: ' ... long to reign over us ... '); 'rein' (also sounding the same) = the thin leather strap used by a rider to control a horse.

Here the problem is that the PAST form of 'read' (in the lower line of the text) sounds identical with the everyday colour 'red'; while the PRESENT form (in the upper line) has the double-EE sound ('You nEEd to rEAd it').
'Every day I usually read the paper ('reeed'), but I don't think I ever read ('redd') yesterday's one.'
There is a similar problem with the word 'lead': as a noun it sounds like 'led' and means the heavy, bendy metal that is used in the making of church roofs etc. (and also ~ wrongly ~ the 'lead' in a pencil). As a verb it sounds like 'leed', as in 'Who is going to lead the procession?'. But the past form of the verb is 'led' (pronounced as you'd expect from the spelling, to rhyme with 'bed': sometimes a person who has rather foolishly let themself be drawn into a bad situation, might be described as 'easily-led'.)

English has two main ways of writing the very common long-E sound: with two e's (as in 'bee' and 'see'), or using -ea- as in 'sea' and 'tea'. (There are other ways again, but let's not confuse matters by dragging those in here.)
We make the 'ch-' sound on words like 'chicken / children / chocolate' with CH-; in French and some other languages, those two letters produce the sound that English spells as SH-, as in 'champagne' (sounds like English 'sham-pain'). Chips and ships are very different things (although in the 1970s, the Royal Navy did run a recruitment campaign using the slogan 'Ships with everything'!).
'Beech' is a kind of tree, often growing in woodlands and having lovely oval leaves that turn copper-coloured in autumn, even more beautifully than many other trees (have a look online for pictures of Burnham Beeches, for instance).
Meanwhile make sure which way round the words are when you travel to the beach ~ that kind of beach, now ~ and 'see the sea'. (Having another common word that sounds like 'sea' is not just an English problem; what about French with not only 'mer', bur also their word for 'mother', and indeed 'maire' for the Mayor of a town?)

We need to keep the Y in a two-syllable word like 'playing' / 'staying' / 'players' etc. (but in the past form 'played' you can no longer hear it). There is no missing letter, hence no apostrophe, in 'fast', nor in 'first'.