Making your Ж and Ш right will improve you pronounciation greatly, and it is already pretty good. Aaand that will be easy. In English SH ("shame") and zh ("pleaSure") sounds are pronounced with your tongue quite close to your teeth, touching the alveolar ridge just behind them. What you need, is slightly "hook" it back. American English "R" gives a good idea about how you do it. Only don't try too hard: certainly, you can curve it all the way back (don't swallow it, though), but the actual difference between tongue tip position in Russian and English SH is very little, less than a centimetre.The point is, the manner of articulation significantly affects the amount of "friction" heard when the air passes through the mouth, which in Russian SH is much less.

Soft "Р" in "время" doesn't sound convincing, but it's difficult to give a specific advice, the consonant is pretty hard as it is. Try acting the same way as with many other palatalized consonants employing your tongue tip: change the tip to the blade. That is, use a sligtly larger area at the upper side of your tongue, including the one just behind the tip, rather then tip alone.

"Исчезнет" is actually pronounced as if it were "ищезнет". "Сч" is one of these standard consonant combination that are usually read slightly differently from how they are spelt. There are many more words with this combination: счастье (happiness), считать (to count), расчёска (comb, brush for combing your hair)
"Скучно" in literary laguage is pronounced with Ш ("скушно"), same as "конечно", but you may very well ignore this one, as "скучно" is heard just as often, if not more often. Actors are trained to say "скушно", though A bit more conservative of a pronunciation. Be aware that "конечно" is different in that "ШН" is stable there. "Конечно" with "ЧН" doesnt mean "of course". It is short form adjective "finite" (rather than infinite, endless).