The marriage cert would give Albert's father's name, then that will help you find him as a child in 1891 and 1901 censuses, which in turn should give a place of birth for him.
Re children of the Bottom/Pykett marriage, the birth indexes are free to search on ancestry - choose the full version. rom 1911 they will give the maiden name of the childes mother, so if you go through systematically quarter by quarter you should easily pick out the children from the marriage. If the area is consistant, then with this unusaul name you should also find likely candidates for the years of the marriage pre 1911.
Re deaths. Again death indexes are free on Ancestry. I know it will take a while, but I cant imagine there are many Amelia Bottom's around, especially as you have an exact age for her, so it would be worth going through the death indexes quarter by quarter till you found her. can look for Albert Edward Botttom at the smae time. At present you know they were both alive in early 1914 (birth of Charles) but you may narrow the possible years further if you find later children.
Happy hunting! That's what family history research is all about - bit so worth it when you find them and it finally all fits together!
Here is the link
http://www.ancestry.co.uk/search/rectype/vital/freebmd/bmd.aspx