Sinae patria mea sunt. In Pechino/Beijing habito.
The noun Sinae is in the plural, and so you get the plural form of the copula, sunt, and not est. If you use the 'Latinized' word Pechinum for Beijing, it has to be in the ablative case because the preposition 'in' takes the ablative when denoting something that takes place in a place, as opposed to movement into a place, where you get the accusative instead: In Italia (abl.) sum, 'I am in Italy', In Italiam (acc.) ibo, 'I will go to Italy'.
Linguam Latinam amo.
Linguam Latinam is in the accusative case. Latinam has to agree with as the noun it modifies (linguam). That means having the same case (accusative), the same number (singular), and the same gender (feminine). Here's an overview of all the possible forms:
Singular
Nom. lingua Latina
Acc. linguam Latinam
Gen. linguae Latinae
Dat. linguae Latinae
Abl. lingua Latina
Plural
Nom. linguae Latinae
Acc. linguas Latinas
Gen. linguarum Latinarum
Dat. linguis Latinis
Abl. linguis Latinis
Quare eam amo? Est quia Vergilium amo.
Nemo me docet. Magistrum habere volo.
Nullus is probably okay here too, but nemo seems to be the more frequently used word.
In Italiam veniam. Quare/cur in Italiam veniam? Litteras Latinas Italicasque discere volo.
You can use litterae in the sense of 'literature'. As above with lingua Latina, Latinas and Italicas have to agree with litteras, i.e. be in the accusative plural. You can also write litteras Latinas et Italicas. Adding -que to the second element is just an alternative way to go about it.
Quare litteras illas amo? Est quia Vergilium et Dantem amo.
Nom. Dantes, acc. Dantem.
Linguam Italicam disco. Lingua Italica facilior est.
You'd probably be better off just using discere, 'to learn'. If you want to state explicitly that it's easier than Latin, you could have lingua Latina in the ablative, which would mean 'than Latin' in this context: Lingua Italica (nom.) lingua Latina (abl.) facilior est.
Lingua Latina difficilis est, verum tamen amo.
Since lingua is feminine, you have to have the form difficilis. If you have a neuter noun you would use difficile.
Sina est patria mea. In Beijing sum.
Amo linguam latinae. < Amo Latina. or Latina mihi placent, since the names of languages are neutral plural. Graeca, Latina, Anglica.> But for Lingua it must be nominative Lingua Latina, the case and gender of the noun and adjective must agree. Linguam latinam amo.
Quare eam amo? Amo Vergilium.
Nullus me docet. Volo magistum.
Ad Italiam veniam.
Quare Italiam veniam? Volo studere litteratum latini et itali. <Literaturam latinorum et italianorum volo studere. >
Quare eos amo? Amo Virgilium et Dantum.
Lingua italiae studeo. Lingua italiae facilior est. <italiana studeo, or linguam italianam studeo. Italiana sunt faciliora, or lingua italiana est facilior >
< linguam italianam studeo, or linguam studeo italianam. >
Lingua latina difficile est. Verum eam amo.
< Latina sunt difficilia or Lingua latina "difficilis" est> Difficile is neuter and Difficilis is nominative common gender for masculine and feminine.
<Latina, linguam difficilem, vere amo. Is what I would say.>
http://en.wikipedia.org/wiki/Apposition
Lingua latina difficile est.
hummm... difficile is adverb... so it's correct^_^