Modern technology/equipment makes all our lives easier.
We've done a lot of research/experiment into why people are scared of spiders.
I'm using a computer research/program that translates from English into Greek.
This drug seems to have no effect/lack on humans at all.
The experiment just involves/operates answering a few questions.
Could you program/estimate how many times a week you eat cheese?
Do you think anyone will ever invent/discover a time machine?
Professor Reinhart decreases/runs the computer lab with her three assistants.
There's a lack/an effect of phones in this office. We need some more!

Modern technology makes all our lives easier.
Правильный вариант: technology. В данном случае речь идёт об общем понятии современных технологий.

We've done a lot of research into why people are scared of spiders.
Правильный вариант: research. Устойчивое выражение — research into something.

I'm using a computer program that translates from English into Greek.
Правильный вариант: program. Компьютерная программа — program.

This drug seems to have no effect on humans at all.
Правильный вариант: effect. Устойчиво: have no effect on.

The experiment just involves answering a few questions.
Правильный вариант: involves. Глагол involve используется в значении «включать в себя».

Could you estimate how many times a week you eat cheese?
Правильный вариант: estimate. Значит «примерно подсчитать».

Do you think anyone will ever invent a time machine?
Правильный вариант: invent. Изобретать новое устройство.

Professor Reinhart runs the computer lab with her three assistants.
Правильный вариант: runs. Run a lab — управлять лабораторией.

There's a lack of phones in this office. We need some more!
Правильный вариант: a lack of. Устойчивое выражение — нехватка чего-либо.