Sandalku basah; tolong lap dengan tisu lalu jemur di pinggir jendela.

Indonesian doesn’t need a be-verb with adjective predicates. An adjective can directly describe the subject:

• Sandalku basah. (My sandals are wet.) Using adalah here is wrong; adalah links two nouns (e.g., Dia adalah guru).

-ku is an enclitic meaning my. It attaches to the noun with no space or hyphen: sandalku (my sandal/sandals). Alternatives:

• sandal saya (neutral/formal)
• sandalku (a bit more intimate/compact) Don’t write sandal ku or sandal-ku.

Indonesian doesn’t mark plurals by default, so sandalku can mean my sandal or my sandals (usually the pair). To be explicit:

• kedua sandal saya (both my sandals)
• sepasang sandal saya (my pair of sandals)
• sandal-sandal saya (my sandals, reduplication for plural)

A semicolon links two closely related independent clauses: a statement followed by a request. You could also use a period:

• Sandalku basah. Tolong lap … A comma is common in informal writing but less standard.

Tolong is a polite request marker, roughly please (help to). It softens imperatives:

• Tolong lap … (Please wipe …) Comparisons:
• silakan: an invitation/permission (Please go ahead), not a request you need done for you.
• mohon: very formal/solemn please (often in notices).
• bisa tolong …?: could you please …? (polite, conversational)

Yes, it’s polite. To soften further:

• Tolong dilap … (passive; very common, service-oriented)
• Bisa tolong dilap …?
• Tolong lap … ya. (friendly)
• Tolong lap … dong. (casual/informal)

Both.

• Noun: lap = a cleaning cloth (kain lap).
• Verb: lap = to wipe. Imperative here is the bare form: lap. Related forms:
• mengelap (to wipe; active)
• dilap (to be/get wiped; passive)
• laplah (imperative with -lah, polite/formal) Colloquial: ngelap (from mengelap).

It’s understood from context (the sandals). Indonesian often omits repeated objects. Fuller versions are fine but not required:

• Tolong lap sandalku dengan tisu, lalu jemur sandalku …
• Tolong dilap dulu, lalu dijemur, ya.

Jemur means to dry something by exposing it to sun or air (often sun-drying). Alternatives:

• keringkan: dry it (general, not necessarily sun)
• angin-anginkan: air it out If there’s no sun, keringkan di dekat jendela or angin-anginkan might be better.

Yes. As an imperative, both are heard:

• Jemur di … (neutral)
• Jemurkan di … (adds a causative -kan feel; also common) Related:
• menjemur/menjemurkan (active)
• dijemur/dijemurkan (passive) Your sentence’s bare jemur is perfectly fine.

Pinggir means edge/side. So di pinggir jendela = at the edge/side of the window (often implying the windowsill area). More precise:

• di ambang jendela = on the windowsill Synonyms for pinggir: tepi (very close in meaning). For near the window: di dekat jendela.

All can mean then, but:

• lalu: neutral, common in writing and speech.
• kemudian: a bit more formal or sequenced.
• terus: very colloquial (and then/and keep going). Your sentence with lalu is natural.

Both mean with/using tissue:

• dengan tisu (neutral)
• pakai tisu (colloquial) More formal: menggunakan tisu or gunakan tisu. Note standard Indonesian spelling is tisu (not tissue).