The letters you were looking for are marked in bold. A modernized version of the sentence is given, and then the translation.
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Ynys y Kedeirn - It can't be "his", "her", or "to" because those would cause some mutation of the "k" ("c" in standardized spelling). It could be a preverbal particle if Kedeirn were a verb, but kedeirn doesn't look like it has any of the usual verbal endings. It's the definite article here, in this case followed by a plural adjective serving as a noun (strong [ones]).
y gyt - The following word could have a lenited "c", or it could have an unlenited "g". Following our mutation rule for final consonants, we look up both "cyd" and "gyd". Under "gyd", you may find the idiom "i gyd" meaning "entirely, together". If not, you look at "cyd" (from which "gyd" is lenited) and find a masculine noun meaning "a joining" or an adjective meaning "joint, united". Since the noun is masculine, our word can't be the definite article (which wouldn't cause lenition); and since it's lenited we're looking at either "his" or "to". In the context of the whole sentence, an adverbial sort of phrase would make more sense than a noun phrase. You may not be able to figure out the precise meaning "together" for "i gyd" unless your dictionary has it, though.
ual y byddynt - Two clues here: as you learned in the last lesson, the preposition val most often takes a verbal phrase following it (although it has a different meaning here than the one you learned); and while you may not currently recognize byddynt itself, you should immediately notice that -ynt ending as being third person plural. So either byddynt is a verb or a conjugated preposition. Looking at your list of prepositions that conjugate, this doesn't look like any of them so it must be a verb. So "y" is almost certainly a preverbal particle in this case.
Y doeth - If you still remember that doeth is the 3sg preterite form of "to come", then you know that our word must be the preverbal particle. (The preposition would only be found in front of a verb if it were in the verbal-noun form.)
y mi - With the pronoun mi (I, me) following, this almost has to be a preposition, and looking at your personal forms of prepositions it matches y meaning "to".
y gan - You already know a compound preposition that looks like this, but also consider other possibilities. Theoretically, gan could also be a lenited form of "can" (song, poem) which is a feminine noun, so the whole could be either "the song" or "his song". Translate the sentence up to this point and see which is likeliest to make sense:
You may not know at this point that you are very unlikely to get a prepositional phrase like "to me" interposed between the verb and the subject (thinking of "the/his song" as a possible subject), but if you look at the very next word (wr) and recognize it as the lenited form of gwr (man), you should remember that you don't get noun phrases of the form <definite article> <noun> <modifying noun>, so this can't mean "the song of a man", and it would make no sense for it to mean "his song of a man" -- what's more neither of these contexts would cause lenition. So you should conclude that it must be "from", which will cause lenition in the following word.
y'th wlat ti - Now that you've been told (in the last lesson) that 'th is an alternate form of dy (your), you should recognize 'th X ti as a noun phrase meaning "your X". So our word can't be a preverbal particle because there's no verb; it can't be the definite article because you wouldn't use that and a possesive pronoun at the same time; and it can't be either "his" or "her" because we already have a possesive pronoun. The only likely thing left is the preposition: "to your land".
att y vorwyn - You've got "<preposition> y <lenited feminine noun>" -- your immediate conclusion should be that this is the definite article.
dodi y law - Given medieval spelling, we don't know whether the "l" represents standard "l" or "ll", or for that matter it could be lenited "gl-". Llaw is the feminine noun "hand", glaw is the masculine noun "rain". We can rule out "the rain" because there should be no lenition, but we're left with "to/the/his/her/their hand" and "to/his rain". If you've looked up "dodi" and discovered that it's the verb "to put, place" then we can use the sensibleness test and try "... and coming to the maiden and putting ???" - well, "rain" seems a little out of place but the only one of the others that can reasonably be ruled out is "their", given that "hand" is singular. Let's wait on this one.
ar y hysgwyd - Upon failing to find hysgwyd or anything resembling it as a word, you should immediately suspect the h-insertion that either "her" or "their" would cause. You then find ysgwyd as an archaic word meaning "shield" and ysgwydd meaning "shoulder". Since it's singular, this is more likely "her" than "their". Thus either "on her shield" or "on her shoulder". And, alas, Medieval Welsh literature has a dearth of warrior women, so we must suspect the latter.
Now let's go back and look for the likeliest interpretation of the last word. "... and coming to the maiden and putting to/the/his/her hand on her shoulder". It looks like we can eliminate the preposition, but we can't narrow it down further without more context. As it happens, in the original text it's clear that the hand belongs to a man.
y chnawd - Even if you didn't recognize this from a previous lesson, the initial "ch-" could only come from an aspirated "c", so our word must be "her", the only one of the group that causes aspiration.
distrych y donn - There is no don(n) listed in the dictionary so this must be lenited ton(n) ("wave" a feminine noun). Since we find distrych as "foam", this looks like an ordinary modified noun phrase: "foam of the wave". While "foam of his wave" is a technical possibility, it doesn't make much sense.
The letters you were supposed to identify are marked in bold. Then I have given a "standardized" version of the text, followed by a translation.
Eyl ev er effeyryat teylu; ef a dely e tyr en ryd a'e uarch pressvel a'e vrethynwysc y gan e brenhyn a'e lyeynwysc e gan y urenhynes. E le en e neuad yv e am y tan a'r brenhyn, en nessaf e'r keluy, vrth uendygav e bvyt a chanu pader.
Eil yw yr offeiryad teulu; ef a ddyly y dir yn ryd a'y varch presswyl a'y vrethynwisg y gan y brenhin a'y lieinwisg y gan y vrenhines. Y le yn y neuadd yw y am y tan a'r brenhin, yn nessav i'r celwy, wrth vendygaw y bwyd a chanu pader.
Second is the household priest; he gets his land freely and his horse constantly and his woolen-clothes from the king and his linen-clothes from the queen. His place in the hall is opposite the fire from the king, closest to the screen, for blessing the food and singing the Paternoster.
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