Перевести в косвенную речь andrew said to me: "i have been learning my part for a week." 2. zac: "i might be late." 3. leyla asked: "where are you going now? " 4. steve asks: "have you taken the breakfast yet? " 5. he told me: "the american film industry began in 1890s in new york." 6. austin: "kill me, please."

Andrew told me he had been learning his part for a week.
Zac said he might be late.
Leyla wondered where I was going then.
Steve asks if I have taken the breakfast yet.
Или
Steve asked if I had taken the breakfast yet.
He told me that American film industry had begun in 1890s in New York.
Austin ordered to kill him.

1) After the accident the injured man recovered consciousness in 
hospital, he remembered crossing the road, but he didn’t remember being  
knocked down. После несчастного случая пострадавший мужчина в больнице пришел в себя, он помнил, как переходил улицу, но не помнил, как его сбили. (после глагола to remember в личной форме герундий в форме Indefinite означает предшествующее действие. Поэтому Perfect-формы здесь не нужны)
  
 2) They lived in a small town for ten years and then moved without making  friends with any of their neighbours. Они прожили в маленьком городе 10 лет и затем переехали, не  подружившись ни с кем из своих соседей.
(После предлогов without, on, after, befor для выражения действия, предшествующего действию, выраженному глаголом-сказуемым в личной форме, употребляется герундий в Indefinite-форме)

3)The juvenile was found guilty of having committed a murder. Несовершеннолетний был признан виновным в (совершении) убийстве(а).

With the development of modern technology, internet let people do a lot of things without going out. One of my favorite is online shopping. .

I think that it's great opportunity to get necessary thing if you don't have enough time. Besides, you can almost always read comments about every product and know opinions of people about it. Many people choose shopping online also because they can’t stand that crowded and noisy environment.

Online shopping does have many advantages but everything has second side. For example, if you order a cloth online, at the moment you get the item, you may find that the color is different from what you saw online, or the size is either too small or too big because it is not available to try on before ordering, or the material of the cloth is not what you want.

I bought many thing on famous shopping site "Aliexpress".Once I needed headphones so I made my order on this site. It had taken about one month before I received my order. But I was ready to that time because I knew that way is too long to get order faster. The headphones were a little worse than I thought, but I was good with them.