"A Welsh shop"
Siop is a feminine noun, so it causes a soft mutation of a following adjective - Cymraeg -> Gymraeg.
(Note that the meaning here is that it is a shop which specialises in Welsh-language things such as books and music, perhaps. A 'Welsh shop' which just happens to be located in Wales and selling anything at all would be a siop Gymreig.)
So, if I understand the difference between the two adjectives,
Cymraeg = pertaining to Wales
Cymreig = from Wales, made in Wales, etc.
e.g. dinas Gymraeg but cwrw Cymreig. Is that correct?
Cymraeg - 1. (noun) the Welsh language. 2. (adjective) Welsh-language, pertaining to the Welsh language.
Cymreig - (adjective) Welsh, pertaining to Wales.
- papur Cymraeg - a Welsh-language newspaper, such as 'Y Cymro'
- papur Cymreig - a Welsh newspaper (language not specified), such as 'the Western Mail', 'Y Cymro' or 'the Abergavenny Chronicle'.
These and other related words (Cymru, Cymry, Cymraes, etc) are explained in one of the 'Hints and Tips', but i can't remember which one just now. A dictionary will explain them all, too.
By and large you need to learn them as you go. There are some guidelines depending on word endings, but there are exceptions to nearly all of them.
For example, most nouns ending in -en are grammatically feminine, but bachgen (boy) is masculine. Most multi-syllable words ending in -aeth are feminine, but gwasanaeth (service) and a few others are masculine. -wr, -iwr, -ydd are usually masculine.
A small number can be either, such as munud, eiliad, trosedd, which vary by dialect, and some such as llif, gwaith, pryd which vary with meaning.