Yes, Ganesh and Kumara both are mentioned in Vedas. Here are the references.
रुद्रो रुद्रश्च दन्तिश्च नन्दिः षण्मुख एव च ।
गरुडो ब्रह्मा विष्णुश्च नारसिहंस्तथैव च ।।
rudro rudrascha dantischa nandi sanmukha eva cha |
garudo brahma vishnuscha narsimhastathaiva cha || [Yajurveda Taitteriya Aranyaka 10.1.15]
The names of God mentioned are:
Rudra, Danti, Nandi, Shanmukha, Garuda, Brahma, Vishnu, Narsimha
As you can see the whole first line mentions the name of Shiva family:
i.e,. Rudra, Danti, Nandi, Shanmukh
Shanmukh (six faced) is another name of Kumara.
Danti(tusked one) is another name of Ganesha. It is also evident from this Ganesha Gayatri mantra mentioned in Taittariya Aranyaka of YajurVeda.
तत्पुरुषाय विद्महे वक्रतुन्डाय धीमहि तन्नो दन्ति प्रचोदयात् ।
Om tatpurushaye vidmahe vakratundaye dhimahi tanno danti prachodayat | [YajurVeda Taittariya Aranyaka 10.1.5 ]
We meditate upon Him who has a curved trunk. May the tusked One guide us on the right path.
As you know Vakratunda is a name of Ganesh and it names also Danti (tusked one) at the same time.
Also Kumara Gayatri is mentioned below it in Yajurveda Taittariya Aranyaka 10.1.6
तत्पुरुषाय विद्महे महासेनाय धीमहि तन्नो षण्मुख प्रचोदयात् ।
tatpurushaye vidmahe mahasenaya dhimahi tanno shanmukha prachodayat.
We meditate upon Him who is great commander (of devas), may Shanmukha (sixfaced i.e., Kumara) guide us on right path.
Yajurveda Taittariye Samhita 188.8.131.52 contains this verse:
नमो गणेभ्यो गणपतिभ्येश्च भो नमो:
namo ganebhyo ganapatibhyescha bho namo |
Salutations to him who is in (Gana) host and who is in Ganapati (i.e., Lord of host)
Also in Rig Veda:
ॐ गणानां त्वा गणपतिं हवामहे कविं कवीनामुपमश्रवस्तमम् ।
ज्येष्ठराजं ब्रह्मणां ब्रह्मणस्पत आ नः षृण्वन्नूतिभिः सीदसादनम् ॥ [RigVeda 2.23.1]
We call thee, Lord and Leader of the heavenly hosts, the wise among the wise, the most famous of all, the King supreme of prayers, O Brahmaṇaspati: hear us with help; sit down in place of sacrifice.
Although the devata of this mantra is Brahmanaspati Veda scholars use this mantra to summon Ganesha as it satisfies all characters of Ganesh.
Some people also equate Brahmanaspati as Brihaspati. Some also say Brihaspati is aspect of Ganesh. But some debate Brihaspati is son of Angiras. Whatever it may be. We are not here for speculation.
But if we go by Jnana Kanda Marga, then Angiras, Brihaspati and Brahmanspati have special meaning. Here is how Brihadaranyaka Upanishad of Yajurveda describes it.
I-iii-19: It is called Ayasya Angirasa, for it is the essence of the members (of the body). The vital force is indeed the essence of the members. Of course it is their essence. (For instance), from whichever member the vital force departs, right there it withers. Therefore this is of course the essence of the members.
I-iii-20: This alone is also Brihaspati (lord of the Rik). Speech is indeed Brihati (Rik) and this is its lord. Therefore this is also Brihaspati.
I-iii-21: This alone is also Brahmanaspati (lord of the Yajus). Speech is indeed Brahman (yajus), and this is its lord. Therefore this is also Brahmanaspati.
Hence if we go by Jnana Kanda Marga:
Angirasa= Anga + Rasa
i.e., Vital fluid of body.
From Vital fluid of mouth(Angiras) comes the speech/Vak shakti (Brihaspati, Brahmanaspati). Hence by Jnana kanda we see them separately. Also Brihaspati is considered lord of Rik and Brahmanaspati considered lord of Yajus.
For the question why Ganesh isn't mentioned in Valmikiramayan. It is because Ganesh wasn't so much popular at that time. He was the chief leader of Gana of Shiva. Kumara/ Kartikeya is mentioned as he is commander of Vedic Gods like Indra. At that time dominance of Indra like God was more as evident from fight between Krishna and Indra when he stopped worship of Indra.
Furthermore if we go by Sabda Brahman Concept people who recite ValmikiRamayan also worship Ganesh. This verse is in Phala Shruti of Yuddha Kanda of Valmiki Ramayana.
विनायकश्च शाम्यन्ति गृहे तिष्ठन्ति यस्य वै ।
विजयेत महीं राजा प्रवासि स्वस्तिमान् भवेत् ।।
Here is the word "विनायकश्च शाम्यन्ति" i.e., Vinayakascha Samyenti. i.e., Obstacles are removed. Although it is not calling Vinayaka. It is just used to denote obstacle. But by Sabda Brahman Concept one doesn't need to be aware of God also when it is chanted as evident from story of Valmiki (i.e., Mara Mara), also evident from story of Ajamila (i.e., Calling his son Narayana). Thus who is reciting Valmiki Ramayana if not aware of Lord Ganesh also then he still worships him. Same case applies in the other mantra where Gods name is used. This is the same reason how the seer of "Gananam tva Ganapatim...." of Rigveda i.e., Grutsduma became a great devotee of Ganesha later.
For the question why Ganesh isn't mentioned in Bhagvad Gita? You have to ask this question to Lord Krishna. Furthermore Bhagvad Gita is only popular in present time, It is just a very small portion of Mahabharata. It became popular after Sankaracharya wrote commentary on Bhagvad Gita. Before that time Hinduism was dominated by Purva Mimamsha which doesn't go for Jnana marga.
For your question who is elder? As far as I know Vedas don't discuss who is elder. I don't want to cite Puranic stories as you don't believe in them.