My question is simple. Does thought or intention alone become karma?
As you implied, in the sutras, karma is defined as volition manifested through body, speech and mind. Karma can be thought as volitional action where "action" is any manifestation of "yourself", either externally visible (e.g. movements, words) or not (e.g. thoughts). Also, it seems that, at least from Buddhaghosa's lens, the volition and the action are not synonyms, but occur simultaneously (and there's no karma [fruits] without volition).
So a volitional thought is karma; is action. But, say, a different action than a physical movement, which is also different action from a utterance.
Or does it need to have certain characteristics (Sorry if this word is inappropriate) for it to become Karma?
It needs volition to be karma, to be a [morally/karmically significant] action.
If intention alone is karma whether we engage in action in though, word or deed what is the point of good deed? Can we just "think" that we are helping the poor and have good karma? Can we "think" that we are giving dhana to monks and have good karma?
A volitional thought of helping someone is a karma of thinking of helping someone; it's fruits are those produced by the thinking of helping someone.
On the other hand, a [series of] volitional action[s] with a disposition of helping someone has as fruits those produced by all the actions that, performed with the disposition to help, helped someone.
The fruits are different, as the actions are different.
Furthermore, it's not the appearance of an action that qualifies the karma (or if some expectations were fulfilled or not, e.g., if someone was helped or not), but whether the karma/volition is rooted in (non)ignorance, (non)hatred, (non)greed.
In the context of good karma, can we just have good intentions and thoughts of good deeds and get the same karma that we get from physically engaging in such activities?
No. Another way of thinking of karma results is the aggregates: your body, consciousness, perceptions, mental faculties, etc. One point of view would be to see "who you are" as the result of your past deeds. In this sense, "you" are the product of your actions (of body, speech and mind).
Conventionally, if you are a person who "frequently thinks of helping people", then you end up becoming such person: "one who frequently thinks of helping people" -- you are not a person who engages in helping people, as helping people is not an activity you've been engaging at; thus, you should expect distinct karmic outcomes.
From my understanding, (and glossing over) how much commitment, time, energy is devoted to some performance, how much it demands from your mental and physical faculties (how much it reconfigures them, or how much it reenforces habits), then that much is the transformation that one suffers [the transformation of becoming], and so, as far as volition is involved, that much fruit is expected to ripen.