1. "to make one more step on my own, alone" 2. After numerals ending in "два", "три" and "четыре" adjectives experience an unusual (for a foreign learner) pattern when the combination is supposed to be in Nominative (or Accusative for inanimate nouns). - masculine and neuter nouns use adjectives in Genitive Plural: два длинных карандаша, четыре добрых человека - feminine nouns can take adejctives in Genitive or Nominative Plural. Some guides recommend Nominative – though, if Gen.Sg and Nom.Pl forms have different stress for the noun (руки́ - ру́ки), Genitive Plural is preferred. Aside from that exception (quite relevant for feminine nouns) it is hard to tell which options is currently preferred. For inanimate feminine nouns I'd go for Nom.Pl ("три длинные флейты"), though I still think both are possible. What may be counterintuitive is that with numerals even feminine nouns will copy their Nominative behaviour when they are inanimate: comapre "Я купил ручку и карандаш" and "Я купил две ручки и два карандаша". And even more than that, the Accusative pattern for animate nouns is somewhat broken for bigger numerals ending in 2/3/4: for such numbers both Nominative and Genitive are sometimes used for Accusative ("Я вижу двадцать три мальчика/двадцать трёх мальчиков", if I did not mess it up). Nominative is easier, probably. Both sound kind of awkward

To add to the answer above, indeed: шип IS singular, шипы is plural. Singular Genitive would be шип, but Plural genitive would be шипa. By the way, you may also say шипов. But шипa is a bit more poetic. The good news is there are very few words that do it. I could not even think of any other right now. Hope this helps!

1) He wants to do one more step alone. As I see it, he means the final step in his life. 2) The rose has just four little thorns. "Жалких шипа" both words are in Genitive Plural.