Your sentences are right ... Prepositions are words that indicate location or direction. They are called pre-positions because they come before the place or direction Common prepositions are 在, 从，到 with locations 从 can also go with time 离 ... 远 or 近 goes with distances 对 indicates targets 给 also indicates targets, but can indicate an action for someone 替 to substitute for or take the place of someone; commonly translated as for ... 被 works with passive constructions

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我把書放(在)桌子上> '' 在......上 '' means on the ...... > 書本在桌子上。 '' 把....放 '': 把 means that you use your hand to take sth, and 放 means to put. 我正在房間裡學習漢語> '' someone+正在+verb'' means someone is doing/verb+ing> 我正在學習漢語。In Chinese, we put usually the place before the verb, so you can say 我正在房間裡學習漢語。

2------------------------------2 3）There is a peculiar syntactic structure in Chinese named locative/positional phrases 方位短语, which consists of a noun + a localizer (上，下，左，右，前，后，东，西，南，北，中，里，内，外；and some other localizers composed by one or two of these words, for instance, 东南), for instance, 桌子上，屋外，海上. Chinese locative phrases can be used by theirselves, （×在）河那边是一大片金黄色的油菜花，煞是好看||| （到）屋里坐（吧），（到）屋里坐（吧）！and used with prepositions as well. When they are used together, the prep. often can be omitted. ------ （我该把_/你想让我把_）书放在哪里？------- 放(在)桌子上吧！ I think your confusion about when to use and when not to use a prep. arises on the occasion where a locative phrase is used. This is an complex problem. I'm sorry to say I havn't did close study on it, so I cannot rashly give a specious answer, though I have some vague ideas about it . Maybe you can find some information over this problem on the internet or some special reference materials.

2----------------1 - 我在房间里正在学习汉语。= I'm studying in my room. - 我把书放桌子上。= I put the book on the table. --- 我正在房间里学习汉语。 --- 我把书放在桌子上，就回来了。|| 我把书放桌子上，你待会儿自己来拿吧。 正，在，正在 all can be used as adverbs. 我正吃饭呢，外面打起雷来了 | ----- 你在干什么？---- 我在买东西。| 我正在打篮球。 In the sentence 我正在房间里学习汉语, 正在 is actually a combination of the adv. 正 and the prep. 在. When the adv. 正在 is followed by the prep. 在, the latter is always omitted. Generally，Chinese prepositions have very simillar use with or even all the same as those in English and French. As a CFL learner, we need to know 1) which are Chinese preposions and what does each mean? In modern Chinese we use about 70 prep.( almost all the same as those in french and english too).They are used in different frequency. 2) what do prepositional phrases function as in sentences. A preposition does not be used solely, it always acts as part of a prepositional phrase. Therefore the problem turns to be what grammatical functions the phrases carry out in sentences. They serve as adverbials 老李找了一把锤子，然后在墙上钉了一根钉子, verbal complements (i.e. postpositive adverbials) 把一根钉子钉在墙上，and attributives 到巴黎的航班马上就要起飞了.