看看这一小段英文有没有问题，高手赐教！！急……在线等！

For the first time I successfully installed an engine into the car I drew and ran it on the screen. Up till now I’ve built various empires one after another on the website. I am always a curious and determined explorer.

from the first time - for the first time
install an engine into a car
the car I drew (有定语从句I drew作修饰时，前面的名词需要定冠词the）
to let (有目的意义，这里用and连接，简单明了的两个动作。）
to today, 迄今为止，你是要这个意思？= Up till now, Till now 后面要求用完成时
varying - various 各种各样的，好多种
one after - one after another
I am always the ... I am always a...无需特指

我想表达的意思是：从第一次我成功给我画的小车装上engine让它在屏幕上跑动（说的是flash,这里用的是比喻），到今天我建立了一个又一个不同的网络王国，我一直是那个好奇且坚定的探索者。
按照你这个意思，我改一下：(123来不及 说的很对，中文的最后一句应该是英文的主题句）
I have always been a curious and determined explorer. I have built many web empires ever since the first time I successfully installed an engine into a car I drew on my computer and made it run on the screen.

我看了你的问题补充，特补充修改意见如下：
1）from the first time