depend：相信; 信赖 依靠,依赖; ; 依...而定
depend on：依赖,依靠,取决于,随 ...而定
第一句我觉得还是有点不妥吧：Tom可以依赖他们（以达到）安全到达这儿（的目的）.
改为：Tom can depend that they will arrive here safely.
第二句我觉得可以.
第三句：
To ensure that you are able to make proper arrangement,we invited you in advance.
we invite you ahead 改为 we invited you in advance.体现了时间且更符合英文表达.