I'm bound to you.

这好像不是一个完整的句子.因为the people是主语,而who are bound to be faced with the same problem we had是定语从句,修饰the people,那么谓语就是get,而getting不能做谓语.
难道had后面一杠横线还要填词?如果能填的话,就变成some day the people who are bound to be faced with the same problem we had（will be）getting rid of this.

mom ,I am bound to make you live happily !

嗯,像这么老的一辆车注定是有缺陷的.
a truck this old相当于an old truck like this 有点倒装的味道
像这么老的一辆车
老外口语中常用的很多句子都不管语法,要从语法分析有的是不对的,但那么说能明白对方的意思.
be bound to 很常用的词组表示“必然,注定.”
因为bind做动词有绑定的意思,所有be bound to就是被绑定成=
“必然,注定.”的意思
A truck this old was bound to have a flaw.
一辆像这么老的卡车总是会有缺点的.
It was a rational plan and bound to succeed.
这是一个合理的计划肯定会成功.
King:Whoever sings like that is bound to be happy!
国王：这位唱歌的人,注定是位幸福的人.
One slogan they are bound to shout is “Customers are our gods”.
他们肯定会喊的一条口号的是：“顾客就是上帝.”
be bound to这个词组很常用,看完例句记住它.以后就都会用了.
语法的话 ,你说的对,this old后置定语修饰truck.
be bound to have 注定有.
分析可以把“有”当成动词,be bound to修饰have的副词

翻译：你准备去哪儿?或者你准备往哪儿开（车）?
bound for 意思是开往,驶往...口语也可以指去哪儿.

if 表假设 并非表示"是否"的意思 所以不用whether
or 也并非是whether...or...句型 而仅是"或者"的意思