Is "shined" correct? If so, is "he shined X on the tree" also correct?

The Grammarist has an opinion on this issue, writing that the difference between the two is as follows:

The verb shine has two main definitions: (1) to emit light (intransitive), and (2) to cause to gleam by polishing (transitive). As an intransitive verb (definition 1), shine makes shone in its past-tense, perfect-tense, and past-participle forms. As a transitive verb (definition 2), it makes shined.

He says that the following are incorrect uses:

• But the one that shined the brightest was simply topped with a perfect beurre blanc and a touch of caviar. [The Atlantic]
• What’s more, one of the numbers reflected light differently when Smith’s headlights shined on it. [Winnipeg Free Press]

The following are correct uses:

• A 13-year-old boy needed hospital treatment after a laser pen was shone in his eyes in Eastwood. [BBC News]

• A return trip to the store shone the light on what I needed: Leeks. [Denver Post]

• Shearer doesn’t look like he belongs ensconced in dark-green leather and spit-shined oak . . . [Washington Post]

• They shined the marble. [National Post]

So if the verb is intransitive, you should use shone. If it is transitive, you should use shined. In your examples:

The light shined all throughout the night.

Here, shine is intransitive, since you're not talking about shining the light on something. So it may actually be better to say "the light shone all throughout the night".

In your second example, "He shined the light on the ball throughout the night" this is actually correct because the verb is transitive.

Prescriptivists like the Grammarist would say that no, you can't use shone transitively. However, in the argument that people could still understand a transitive shone, you could use it. It is up to you which side you'd want to take on this.

Merriam-Webster's dictionary of English Usage says that in England, in the 16th century, shined and shone were competing past tenses for shine. It also explains that since then, the British and the American usages have diverged. In the rest of the post, I summarize the usage explained in this text (using some of their examples). I have estimated the frequency of these usages myself using Google Ngrams.

In the U.K., shined appears to be used only for the sense of polish, mainly for shoes, and even then only occasionally. See this Ngram for evidence that even for shoes, while Brits are willing to use shine in the present tense, they avoid using shined in the past tense, preferring polished.

In America, for the sun, shone is almost always used. For other sources of light, when shine is used as an intransitive verb, the past tense is shone maybe 90% of the time:

That hard fierce light of publicity that everybody hates shone on everything he did.

But when it is used transitively (somebody shined something), Google Ngrams shows that somewhere around 40% of Americans use shined. This usage started somewhere around 1940, and has been growing in frequency since.

Elated researchers shined their lights around the hilly prairie dog towns.

And finally, when the the word shine has the meaning polish, Americans almost always use shined.

The OED reports that the past participle of shine is "shone, (now especially in sense 8) shined."

The sense 8 to which the dictionary is referring is the following one:

verb transitive. Put a polish on or give a shine to (shoes etc.).

M. French: They…sold newspapers, shined shoes, ran errands.