I'm not very versed in poetry, but I'll see what knots I can untie for you.
Cornelius, to you, for indeed you were accustomed to
Think my [books] to be trifles,
(tu solebas) "meas esse aliquid putare nugas" = "you were accustomed to think my trifles to be something," i.e., Cornelius had a high opinion of Catulus's work, which the author humbly describes here as "triffles." Try "tu solebas putare meas nugas esse aliquid."
Now then when you alone have been daring of the Italians
At all time to explain three volumes,
You have been taughtâ€”Jupiter!â€”and with laborious????
"iam tum, cum ausus es unus Italorum / omne aeuum tribus explicare cartis / doctis, Iuppiter, et laboriosis." = "now then, when you alone of Italians had dared to describe all time in/with three volumes, learned--Juppiter!--and laborious."
As you've probably now noticed, what tripped you up is the "volumes" element, which is a ablative of description and slit over two lines: "auses es explicare omne aeuum tribus doctis laboriosis[que] cartis."
May it remain one more lasting with an age.
(quod, patrona virgo) "plus uno maneat perenne saeclo" = "Muse, let it be everlasting for more than one age."
Obviously the literal English here is a little awkward thanks to "perenne," which I believe is a neuter adjective modifying "quod," which refers to his work. Neuter connecting relatives likes this are common when referring back to previous statements, etc. E.g., in English you'll say "which" to refer to everything you've been saying before hand. Read "uno saeclo" in the ablative of comparison with "plus," "more (than)."
2. How Many Kisses
You seek how many kisses for me
For you, Lesbia, they may be enough and to spare.
"Quaeris, quot mihi basiationes / tuae, Lesbia, sint satis superque." = "You ask how many of your kisses, Lesbia, for me are enough and more/to spare."
The "quaeris" turns this sentence into an indirect question, and this explains the existence of the subjunctive "sint." Read "tuae" as the genitive "(kisses) of yours" and not the dative.
How great a number of Libyan sand
Bearing laserpicium lies in Cyrene,
"quam magnus numerus Libyssae harenae / lasarpiciferis iacet Cyrenis" = "as great a number of Libyan sand lies at/in Silphium-bearing Cyrene."
Here, read "lasarpiciferis" as an adjective of "Cyrenis."
Or how many stars, when night is silent,
Stealthy of men see loves,
So by you to kiss many kisses
"aut quam sidera multa, cum tacet nox, / furtivos hominum vident amores: / tam te basia multa basiare" = "or how many stars, when night is silent, see the secret/stolen loves of men: to kiss you [is] so many kisses"
Read "furtivos" with "amores" as the object of "vident." Next, try "basiare te [est] tam multa basia." The trick is to figure out that "te" is the accusative, not ablative. Also, an "is" is understood in this line. "To kiss you is so many kisses," i.e., too many to count... as many as the sand on the beach or the stars in the sky. "tam" is often pared with "quam" when comparing quantities, which you find a few lines earlier;" "how many ... so many."
Overall, well done! Bene factus es! The variety of mistakes you made are common to those at your level, and while they seem completely debilitating now, they are the sorts of things that get ironed out with practice. Namely, when you're still fresh from the grammar books and just trying to keep everything straight in your head, you've yet to learn what is often called the mental "flexibility" or "open mindedness" needed to read Latin (especially verse!). One tries to pin down certain constructions (cf. "doctis") and can't make any sense of anything; only later one learns that another reading with a word on another line makes everything click. Often, the problem is trying to read words as separate entities that in reality form one sematic unit. These syntax issues are best learned through reading, and the more you do the easier it will become!